Running head: ONCHAIN LOTTERY

The Onchain Gambler: Price Sensitivity and Jackpot Seeking in Blockchain Lotteries

Kahlil Simeon-Rose

kahlil.simeon-rose@wsu.edu

Carson College of Business, Washington State University

915 North Broadway, Everett, WA, USA, 98112

Funding Statement
No funding was received for this research.
Declaration of competing interest
The authors declare the following financial interests: In the three-year period from 2022 to 2025,
KS received research funding from the Cambridge Health Alliance, Division on Addiction;
travel support from the German Foundation on Gambling Research, consulting payments from
APCO, Eilers & Krejcik Gaming, Scientific Affairs, Victor-Strategies, MGM Resorts, and the
General Commercial Gaming Regulatory Authority; and he received expert witness payments
from Benjamin Leigh Carter.
Biography
Dr. Kahlil Simeon-Rose is an Associate Professor in the School of Hospitality Business
Management. His research focuses on public policy and consumer behavior in gambling
industries, including casinos, sports, online, and crypto.

Abstract

Blockchain technology facilitates novel forms of online interaction and commerce,

including unregulated gambling markets. Understanding user behavior within these

environments is crucial, yet empirical research is limited. This study investigates consumer

behavior in a large-scale, blockchain-based lottery, examining whether established psychological

drivers of lottery participation persist in this technologically distinct context. Leveraging

granular, publicly available wallet-level transaction data over 18 months, we analyze the

influence of jackpot size, participation cost, and recent jackpot winners on ticket purchasing. A

novel instrumental variable approach is used to address potential endogeneity, and is

complemented by qualitative analysis of user discussions. Results across models indicate that

behavior mirrors traditional lottery findings and hypothesized relationships: participation

increases significantly with prize pools and decreases with higher costs of entry (including

nominal ticket price and blockchain transaction fees). These findings suggest that core

psychological mechanisms driving gambling behavior, such as attraction to large payoffs and

multiple motivations, may be transferable to blockchain environments. The study highlights the

utility of blockchain data for granular behavioral analysis and underscores the need to consider

human behavior and potential risks when designing and regulating computer-mediated gambling

applications in decentralized platforms.

Keywords: blockchain; lottery; cryptocurrency; gambling; metaverse

The Onchain Gambler: Price Sensitivity and Jackpot Seeking in Blockchain Lotteries

Blockchain technology facilitates novel forms of online interaction and commerce,

leveraging unique attributes like security, transparency, decentralization, and trustless

transactions to potentially transform various sectors (Al-Megren et al., 2018; Ante, 2025; Casino

et al., 2019; Kimani et al., 2020). Its impact on financial services and consumer products,

including unregulated markets like online gambling, creates unique challenges and opportunities

for studying human behavior in digital environments.

Despite blockchain's growing prominence, empirical research into its impact on

individual consumer behavior remains scarce. Much of the existing literature focuses on

institutional applications or the technology's macro-level potential, leaving a significant gap in

understanding how users interact with and make decisions within blockchain-enabled ecosystems

at a microeconomic level. This lack of empirical investigation, particularly concerning consumer

behavioral aspects, limits insights into the adoption, use, and potential consequences of these

emerging digital platforms. For researchers, exploring blockchain's role in product design is

important, as the technology disrupts traditional consumer relationships and redefines

transactional processes, presenting potentially meaningful differences to existing paradigms.

A challenge to this research has been the lack of consumer adoption of onchain services,

driven in-part by regulatory constraints. However, one industry that accrued meaningful

consumer interest is online gambling. For example, a single gambling site that used

cryptocurrencies for payment processing is reported to have produced revenue of $2.6 billion in

2022, higher than many regulated alternatives (Barnes & Chipolina, 2023). At one point in 2022,

that lone operator reported that it was responsible for “5.9% of all Bitcoin transactions; 12.3% of

all Dogecoin transactions; [and] 15.1% of all Litecoin transactions” (Eddie, 2022). Aside from

decentralized finance, gambling may be the industry most benefiting from onchain technology.

Blockchains present several characteristics that make them desirable to gambling service

businesses (Casino et al., 2019). First, transparency and fairness are highly valued in gambling

(Gainsbury et al., 2013), and smart contracts offer a provable, immutable record of each

transaction, which can help eliminate disputes and provide a clear audit trail in the absence of

regulatory oversight (Breidenbach et al., 2021). Second, the decentralized nature of blockchain

eliminates the need for intermediary financial service providers and makes the services difficult

to restrict by law enforcement. This makes the marketplace borderless and less impacted by

jurisdictional constraints, sales taxes, and other market actors found in regulated markets. Third,

the use of cryptocurrencies that are enabled by blockchains creates a global market, as they are

not bound by the same restrictions and regulations as traditional fiat currencies. Last, there

appears to be meaningful overlap between blockchain users and traditional gambling consumers

(Mills & Nower, 2019; Philander, 2023; Steinmetz, 2023), creating a potentially large audience

for gambling products onchain.

Understanding whether onchain gambling products exhibit similar traits to regulated

markets is important to identifying potential risks or protections needed for consumers in these

largely unregulated spaces. It is also advantageous to researchers, as transactional data is publicly

available from blockchain ledgers (Scholten et al., 2020). In this research, we studied the largest

crypto-lottery game on a public blockchain, PancakeSwap Lottery V2, to understand whether it

shared the market wide characteristics commonly observed in regulated lottery literature. We

estimated the effects of jackpot prize pools on demand, and consumer responses to large jackpot

wins. In addition, we exploited variation in cryptocurrency prices and transaction costs to test

consumer responses to changes in the nominal price of lottery tickets, which has not been

possible in traditional lotteries. To do so, we used transactional data collected through onchain

activity.

Our contribution is both empirical and methodological. By leveraging the inherent

transparency of blockchain, we analyze lottery participation at an unprecedented level of

granularity, the individual wallet, providing evidence beyond traditional studies that necessarily

were reliant on data aggregated at the store or jurisdictional level. To our knowledge, this

represents the first empirical investigation of a conventional game of chance operating entirely

within a blockchain. Our approach of linking draw-level characteristics to wallet-level

transaction data provides a novel methodology applicable to broader behavioral research in

onchain markets and environments. Ultimately, enhancing the understanding of user dynamics

within blockchain-based gambling can guide the development of fairer and potentially less

harmful digital entertainment models and inform policymakers navigating the regulatory

challenges posed by these decentralized platforms.

Related Literature

Evidence of lottery play appears in literature as early as the Old Testament, Greek

Mythology, and the Han Dynasty (Kynnersley, 1885; Willmann, 1999) with more modern lottery

designs occurring during the Roman empire (Willmann, 1999) and in Europe during the 16th

century (Ashton, 1893; Willmann, 1999). After an extensive period of lotto draw game expansion

in the second half of the 20th century (Coughlin et al., 2006; Perez & Humphreys, 2013;

Willmann, 1999), lotteries are now ubiquitous. Altogether, the World Lottery Association reports

that it has 156 lottery members and $284 billion in annual revenue among members globally

(World Lottery Association, 2022).

Academic models of lottery consumer behavior generally attribute consumer interest to

one of three explanations: 1) An entertainment based model, where participating in the lottery is

viewed as a form of leisure activity that brings excitement and fun (Burger et al., 2016; Kearney,

2005; Kocher et al., 2014; Perez & Humphreys, 2013); 2) A cognitive bias model, where

participation is rooted in distorted cognitions and misconceptions about probabilities of winning

prizes (Griffiths & Wood, 2001; Hansen et al., 2000; Kahneman, 2003; Langer, 1975; Miyazaki

et al., 2001); and 3) A Friedman-Savage utility model (Friedman & Savage, 1952), which

proposes that utility derived from an increase in wealth that is both convex and concave at

different levels, which explains why individuals are willing to pay small amounts of money for

the opportunity to win large prizes that are ‘life changing’ (Ariyabuddhiphongs, 2011; Forrest et

al., 2002; Kearney, 2005; Perez & Humphreys, 2013). Each of these models has empirical

support, but it seems likely that they must be considered collectively to fully explain consumer

behavior (Perez & Humphreys, 2013).

Many studies of lotteries attempt to measure demand elasticity, generally finding that

demand is inelastic unless high take out rates near 50% are reached (Forrest et al., 2000; Gallet,

2015; Grote & Matheson, 2013). In this context, elasticity refers to the expected value of a ticket,

defined as the difference between the nominal ticket price and the expected return of the ticket in

the draw (Combs et al., 2014; Grote & Matheson, 2013; Kearney, 2005; Perez & Forrest, 2011;

Rodgers, 2020). This is referred to as the effective price model and is largely possible to estimate

due to variation in expected value that is produced by rollover prizes that accrue to future draws

when no jackpot winner occurs (Farrell et al., 2000; Perez & Humphreys, 2013). Baker et al.

(2020) viewed this estimation approach as insufficient and argued that since expected value is

typically less than the ticket price, the decision to buy must also driven by other properties that

standard estimation strategies cannot estimate due to endogeneity problems from a lack of

additional instruments. Endogeneity arises because lottery sales are influenced by the

characteristics of the prize distribution, which are simultaneously affected by the level of sales.

This seems plausible, as consumers must approximate expected value and will do so with a

margin of error that may be skewed. For instance, regarding a lottery with a takeout rate of 52%,

Kearney (2005) found that only 22 percent of National Opinion Research Council survey

respondents estimated the takeout rate to be 'about half', while 70 percent guessed it to be a

‘quarter or less’ and 8 percent guessed ‘three-quarters or more’. Baker et al. (2020) correct for

endogeneity in their Spanish lottery data by using a ‘self-consistent regression’ solution, which

exploits the unique lottery property that the impact of the sales on the prize distribution is

deterministic and known.

Skewness is more generally described as one of the most consistent results in the

empirical literature, a preference of lottery players for large jackpots (Grote & Matheson, 2013;

Perez & Humphreys, 2013). Forrest et al. (2002) most clearly articulate the case for jackpot size

importance, noting in a study of the UK National Lottery that the largest possible prize effect

tends to dominate expected value in terms of importance to demand. This model helps to explain

earlier results from Cook and Clotfelter (1993), Forrest, Gulley, and Simmons (2000), and others

(Perez & Humphreys, 2013) who provided evidence that consumers were more likely to

participate in lotteries with larger jackpots, even when the odds of winning were lower.

Lockwood et al. (2021) extend these findings and show that demand responds more to a change

in the maximum jackpot expected value than it does to a similar change in second prize expected

value, implying a preference for skewness and big wins. This motivates our first hypothesis.

H1: Lottery ticket sales are positively related to the jackpot size.

While much research focuses on the effective price of a lottery ticket, defined by its

expected value, the nominal ticket price itself is notably absent as a direct variable of study in the

provided text. This is interesting because the nominal price is the most salient cost to the

consumer at the point of purchase, representing a fixed outlay regardless of the complex

probabilities and potential returns. However, the challenge in measuring the price elasticity of

lottery games is that there is typically little variation in the ticket price to exploit, and when

variation does occur, there are often confounding changes in other product characteristics

(Combs et al., 2014; Perez & Humphreys, 2013). We exploit novel variation in our data and test

the nominal price of lottery tickets in our second hypothesis.

H2: Lottery ticket sales are negatively related to the ticket cost.

One phenomenon that tends to replicate across games of chance is the representativeness

heuristic, where gamblers interpret short-term outcomes as representative of the long-run odds of

winning (Goodie et al., 2019; Kahneman & Tversky, 1972; Philander et al., 2019). In lotteries,

several studies identify the existence of a ‘halo effect’ that occurs after a jackpot is awarded as

evidence of representativeness. The ‘halo effect’ describes a short-term persistence in increased

sales despite prize pools returning to normal (Farrell et al., 2000; Forrest & Pérez, 2015).

Matheson & Grote (2005) attribute this phenomenon to the publicity following the award of a

prize, though Guryan & Kearney (2008) expand on these results and show that part of the higher

demand may be attributed to a false belief that the winning store is lucky. They find that same

game sales at the winning store increase 37.7 percent in the week following the winner. In

framing our final hypothesis, we examine crypto lotteries for evidence of a halo effect.

H3: Lottery ticket sales are positively related to a jackpot winner in the prior draw.

Methods

Study Setting

PancakeSwap Lottery V2 is examined in this study. The crypto-lottery was created by a

pseudonymous group of one or more developers (PancakeSwap Intro, 2020/2022). The wider

PancakeSwap platform contains several other Web3 products, including the most visited

decentralized exchange on any smart contract blockchain (CoinGecko, 2023). The site appears to

have begun as a fork of the Uniswap decentralized exchange and has since evolved into different

product categories (Zinsmeister et al., 2019/2019). The PancakeSwap platform issues a

‘governance’ cryptocurrency token named CAKE that is described as a multi-purpose token that

can be used to vote on changes to the PancakeSwap ecosystem protocols, participate in new

token launches and NFT minting, earn other tokens, or play in the lottery (PancakeSwap, 2022b).

To make changes to the smart contract code, a majority of CAKE holders must vote onchain in

support of the change. CAKE is a fungible token that follows a BEP-20 standard that is based on

the ERC-20 standard (Liu et al., 2019/2022; Vogelsteller & Buterin, 2015) and actively trades on

both centralized and decentralized exchanges. Accordingly, it is a straightforward process to

convert CAKE into other cryptocurrencies or US dollar stablecoins.

Compared to typical lotto games, the PancakeSwap lottery has a fairly simple design.

Prior to a draw, users can manually or randomly select a six-digit ticket numbers. To determine

winners, six integers from the set {0:9} are randomly drawn in sequence with replacement and

prizes are allocated based on the number of consecutive matching numbers. For example, to win

the two-matching numbers prize, a ticket must match both the first number and the second

number in order. Accordingly, the probability of winning the Match ‘x’ prize is given by the

formula, 𝜌! = 0.1! . The lottery uses the Chainlink Verifiable Random Function system to draw

the numbers. This mechanism provides random number generation that can be verified by

interested parties onchain (Breidenbach et al., 2021). The lottery code is open source and is

described as audited for errors by two Web3 security firms (PancakeSwap, 2022c).

Unlike many draw lotto games, there is no cap to the jackpot prize and it increases

linearly with sales. The lottery prize pool follows the following allocation schedule: 1-match, 2%

of pool; 2-match, 3% of pool; 3-match, 6% of pool; 4-match, 10% of pool; 5-match, 20% of

pool; 6-match, 40% of pool. The remaining 20% of funds is sent to a ‘burn’ pool that

permanently removes the CAKE from circulation. The burn feature is portrayed as a mechanism

for value capture by the overall ecosystem (PancakeSwap, 2022a). The burn feature acts like a

take-out rate in typical lottery game.

Tickets for the lottery cost roughly five US dollars each but are priced in CAKE. Since

the price of CAKE is volatile, the price is set at the beginning of the ticket sale period and will

vary with the USD-CAKE exchange rate until the draw. This provides variation in the nominal

price. Players can also receive a discount on the ticket price if they purchase more than one ticket

per draw. The discount escalates by a linear path from zero to 4.95% if 100 tickets are purchased:
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 =

𝑛 "#$%&'( ∙ 0.0495

Where 𝑛 "#$%&'( equals the number of tickets purchased by a given Binance Smart Chain wallet

for a given draw. Although transactions occur in CAKE, the lottery prizes on the main landing

page are shown in US dollars (see Figure 1, left). Participants must also pay a variable

blockchain use fee known as ‘gas’ that is used by the Binance Smart Chain to prioritize

transactions when space on the blockchain is scarce. When confirming the transaction, wallets

will typically display the estimated gas fee in US dollars, but the fee is paid in Binance Coin

(BNB, see Figure 1, right).

Figure 1 - Landing page for PancakeSwap Lottery (left); Metamask wallet notification for ticket
purchase (right).

If multiple winning tickets are sold in any of the match categories, the CAKE for that

matching sequence is shared equally among the tickets. If no winning tickets are sold, the CAKE

will rollover into the next draw. The mean rollover is 64.97% (SD = 7.21%) of the prize pool. In

addition, 5,000 or 10,000 CAKE is typically added as a bonus to every second drawing, but this

amount is not consistent.1 The lottery typically has a positive expected value, although the lottery

Governance tokens are often used as an incentive to bootstrap participation in decentralized applications
(Fan et al., 2023).

cannot be exploited in practice as the required 20% burn of ticket sales would lead to a negative

expected value if a player purchased every ticket combination.

Due to the structure of the lottery, the expected value of a ticket in US dollars can be

described as a function of the prize pool, the number of tickets sold, and the cost of the ticket.
)

𝜌! ∙ 𝑍 !
𝑒𝑣 = 5
− 𝑇𝑖𝑐𝑘𝑒𝑡 𝐶𝑜𝑠𝑡
1 + 𝑁 ∙ 𝜌!

!*+

Where x is the number of matched numbers, 𝜌! is the probability of matching x numbers, 𝑍 ! is

the prize allocation for matching x numbers, N is the number of other tickets sold, and Ticket

Cost is the price of a ticket in CAKE adjusted USD and the gas transaction costs in BNB

adjusted USD.

A V1 version of the PancakeSwap Lottery pre-dated V2 but used a different mechanism

to facilitate the lottery system that relied on non-fungible tokens (NFTs) as the primary

mechanism to represent lottery tickets and determine the winners. The NFT-based lottery system

added an interesting collectible aspect to the game, but had higher transaction fees and

complexity in managing NFTs for participants (PancakeSwap, 2021). PancakeSwap decided to

transition to the V2 product reduce transaction costs and improve the user experience. On April

28, 2021, the final CAKE incentive into V1 of the lottery occurred and the lottery was paused

until V2 launched on July 6, 2021. During those 69 days, 350,000 CAKE in bonus rewards

accrued from missed lottery injections, which were allocated to the first week of V2 lottery

draws.

At the beginning of the V2 series, lottery draws occurred roughly every 12-hours but later

the frequency was changed to alternate between 12-hour and 36-hour gaps, i.e. twice daily, every

other day (PancakeSwap, 2023). Some draws during the period did not occur at exactly the

scheduled time due to execution errors by the ‘deployer’ smart contract that engages the lottery

smart contract or due to downtime in the Binance Smart Chain.

Content Analysis Study
Methods

The objective of this study was to qualitatively explore consumer interests in various

aspects of the PancakeSwap Lottery, using the platform’s primary Telegram channel, in support

of the quantitative analysis. The focus was to examine lottery-related messages and explore

themes related to instances of consumer interest in jackpot size, expected value, price, and recent

jackpot winners, to understand their potential relevance to the quantitative empirical study. Given

the exploratory nature of this research, we targeted an active subset of users on Telegram,

recognizing that their perspectives may not fully represent all lottery participants.

Data

The data source for this research was the English language PancakeSwap channel on

Telegram. Telegram is a popular communication platform for blockchain users and PancakeSwap

uses it as its platform for interacting with consumers. PancakeSwap asserts that there is no

customer support for users but also direct individuals with issues to their Telegram channel

where there are over 69,000 members and support is often provided by pseudonymous

administrative accounts to pseudonymous users (PancakeSwap, 2022c). Chat logs from the main

channel were exported directly from the Telegram application. Data collection was confined to

the first three months of operation from July 5, 2021 to October 4, 2021. The chat logs were

imported into R for data cleaning and preliminary analysis using jsonlite (Ooms, 2014; R Core

Team, 2023). Since the Telegram channel is used for the entire PancakeSwap ecosystem that

includes non-lottery products, we filtered the results to include only messages containing a word

beginning with 'lott'. To ensure relevance, the filter was tested on a sample of unfiltered

messages, confirming minimal loss of lottery-related content. In total, 174,927 messages were

retrieved from Telegram, 1,397 remained after selecting lottery-related messages, and 1,250

remained after removing moderator comments or channel announcements.

Coding and Analysis

Following the initial processing, manual coding was performed for detailed content

analysis. Messages were categorized according to a pre-established coding scheme. Coding was

conducted by a single researcher with multiple passes to ensure consistency. The coding

categories were as follows:

Interest in jackpot size; messages explicitly mentioning or discussing the size of the
jackpot or total prize pool.
Interest in expected value; messages discussing the expected return or value from
participating in the lottery.

Interest in price; messages focusing on the nominal price of a lottery ticket.

Interest in recent jackpot winners; messages discussing or referring to recent jackpot

winners.

Each message could be coded into multiple categories. The coding process was iterative and

reflexive, allowing for the coding scheme's revision if relevant new themes emerged. Following

the completion of coding, coded data were analyzed to identify patterns and trends. Data were

evaluated qualitatively and quantitatively, with frequency counts of coded categories to

determine the most common areas of consumer interest.

Results

Our analysis of messages from the PancakeSwap Telegram channel revealed notable

patterns of consumer interest related to common lottery themes. Overall, the most common

theme was interest in the jackpot size, followed by recent jackpot winners and nominal price.

There was little interest in the expected value of the draws although many users were interested

in the odds of winning a prize.

Interest in Jackpot Size

Discussion regarding the size of the jackpot was the most common theme in the analyzed

messages, comprising a total of 27 of the coded comments. Users often expressed enthusiasm

about large prize pools: “New Lotto is looking good! Prize pot is currently over 23K Cake!”.

They also expressed disappointment in response to perceived smaller pools: "It seems, intrest

(sic) in lottery going down. It used to be 1m-2m before” and “I don't get the point of lottery, it's

too small pot”.

Interest in Recent Jackpot Winners

Discussion of recent jackpot winners constituted a total of 26 of the messages. Users

expressed curiosity, excitement, or skepticism about recent winners. Messages showed an

interest in knowing if anyone had won a large prize, “Has anyone won big on [PancakeSwap]

lottery?” and if anyone on the channel had won a prize, “Has anyone here actually won the cake

lottery and if so when and how many tickets did you buy?”. There was also a general interest in

being able to access and track results from past draws. A typical message was, “Is there any way

to filter down the addresses who have won the lottery under match 4, match 5?”

Interest in Price

Price-related discussions were found in 23 of the messages. These were mostly queries

about the change in price from V1 of the lottery. A typical message was, "How much cake is

required to participate in lottery?" and “Make a $1 lottery draw! That's what you originally

promised!”. However, there was some awareness of US dollar price in relation to CAKE price,

“I love how it's getting cheaper to enter to lottery as cake rises,” and the costs associated with

paying gas fees, “How much BNB do I have to have to buy a lottery ticket to pay the fee?”

Interest in Expected Value

Only two messages were categorized as related to expected value and neither directly

discussed the concept as described in the lottery literature: “Where can I find the lottery

economics? How much is injected from emissions, what happens when there is no winner in a

category etc” and “Is there a good site which analyses the odds and the best strategy for the

pancake lottery?” However, after an initial review of the messages, an additional category of

interest in the odds of winning was added to the coding scheme due to its prominence in the

discussions. A total of 26 of the coded messages reflected an interest in the odds of winning the

lottery. Several users inquired about or debated the odds of winning the jackpot, suggesting that

many participants are not merely attracted to the potential payout but are also considering the

probability of winning when deciding whether to participate. Messages like "Has anyone

calculated the odds of getting all 6 numbers in order in the lotto, I was thinking it’s just 1 in 10^6

but I feel like the order has a part to play" and "Anyone [know] the probabilities of winning in

cake lottery?" were common.

Discussion

Interest in jackpot size emerged as the most common theme, followed closely by

discussions around recent jackpot winners, and the price of participating. Contrary to what might

be predicted by the effective price model, there was minimal actively discussed interest in the

expected value of the draws. However, a significant number of users showed curiosity towards

the odds of winning a prize.

Users expressed their enthusiasm or disappointment regarding the jackpot size. They

were excited about large prize pools and showed disappointment in response to smaller pools.

This suggests that the size of the jackpot is a significant motivator for lottery participation.

Discussions around recent jackpot winners revolved around curiosity, excitement, and

skepticism. Users were interested in knowing about the experiences of big winners and whether

anyone in their community had won. The ability to track and access past draw results also

appeared to be an area of interest. The success of others may have an impact on users' decision to

participate in the lottery.

Price-related discussions were common, with many users showing awareness of the

changes in price from V1 of the lottery. Messages showed that users were not only mindful of the

nominal price of a lottery ticket but also of the cost associated with paying gas fees. This

awareness suggests that some users are considering the full cost of participation, not just the

ticket price.

Empirical Study
Overview

This empirical study leverages a unique feature of blockchain lottery data: the ability to

track transactions at the individual wallet level. A Binance Smart Chain wallet allows users to

manage their cryptocurrencies, interact with smart contracts, and connect with applications on

the Binance Smart Chain. Each wallet is associated with a unique public address, which serves as

an identifier on the blockchain. These addresses do not necessarily reflect unique individuals, as

a single user can create and manage more than one wallet. For example, some users may create

multiple wallets to enhance their privacy or security. However, barring a loss of private keys, a

person that controlled a given wallet at time t can be reliably viewed as the same subject at time t

+ 1, which makes the data amenable to panel methods. We therefore linked every ticket purchase

to its private wallet address.

Data Period

Data for the lottery draws was extracted using a public remote procedure call node

maintained by binance.org (Haarstad, 2021/2022) in Python 3.11. Since the first seven draws of

the lottery were non-public (PancakeSwap, 2021), we excluded those observations from

consideration and retrieved data on each lottery draw from July 6, 2021 to December 7, 2022.

The draw data includes the time of the draw, the draw round, the number of tickets sold, the total

prizes, the number of winning tickets, and the ticket price. In total, the initial data set includes

734 lottery draws. We collected wallet-level data using Dune Analytics (Dune Docs, 2021/2023),

which produced the number of tickets purchased by each wallet address for each draw. Out of

734 draws that occurred during the time period, there were 198,027 unique wallets. The median

wallet played only one draw, but as shown in Figure 2, there were many participants in multiple

draws.

Figure 2 – Frequency of Lottery Participation by Wallet Address

Measures

The measures used in our empirical modeling include the following variables:

Tickets Sold. The total number of tickets purchased. Quantities reported may refer to the total

number of tickets sold in a draw across all players or the number purchased by an individual

wallet address for a given draw. The wallet level quantity is the dependent variable in all models.

Prize Pool. The primary variable to measure jackpot size, prizes includes all entry fees, CAKE

that rolled over from prior draws, and all bonus CAKE added to the pool for that given draw in

US dollars. The ‘Match-6’ jackpot size is equal to 40% of the prize pool.

CAKE Price. The price of the CAKE token for a given draw (Ryan & Ulrich, 2022). Since

draws are scheduled at times that alternate between 00:00 UTC and 12:00 UTC, the CAKE price

used was the daily opening price for the 0:00 draw, and the average of the daily opening and

closing price for the 12:00 UTC draw.

Ticket Price. The price per ticket in US dollars for a given draw at the time of the drawing,

converted from the CAKE price (Ryan & Ulrich, 2022).

Gas Costs. The estimated fee in US dollars required to execute a lottery ticket purchase on the

Binance Smart Chain at the time of the draw. The fee is computed as the product of the average

daily gas price on the day of the draw (BscScan.com, 2023a) and the gas limit programmed to

execute the buyTickets function of the lottery contract (PancakeSwapLottery, 2020/2023).

Total Cost. The sum of the Ticket Price and Gas Costs, which reflects the entire amount paid to

participate in the lottery.

Blockchain Transactions. The average daily number of transactions on the Binance Smart

Chain (BscScan.com, 2023b) on the day of the draw. This variable is a proxy for general

blockchain activity.

Hours since Prior Draw. Since draws do not occur at even intervals, ‘Time from Prior Draw’ is

computed as the difference in hours between draw number n and draw number n + 1. The

variable is intended to model variation the size of the time window to buy tickets.

Match-6 Winner. The occurrence of a jackpot winner of the prize pool with all six correct

numbers.

Second Lottery. A binary variable denoting the launch of a second lottery product in the

PancakeSwap ecosystem on August 8, 2022. The second lottery operates similar to a prize-linked

savings account, offering random prizes without risking the principal deposited.

Figure 2 illustrates the values of the key variables during the period of study. There were

signs of much different levels during the first week of the lottery when large bonus incentives

were added to the prize pool as a marketing incentive to attract attention and participation. We

removed this week of outliers from the data to avoid biasing our estimates.

Figure 3 – Line plots for time-series data. The first fourteen periods are affected by one-time
incentives and advertising to launch the product (PancakeSwap, 2021).
Table 1 reports the summary statistics of the model variables, excluding the initial outlier

period and a correlation table is provided in Appendix A.

Table 1 – Summary Statistics of Draws
Variable
Tickets Sold (per Draw)
Ticket Price
Prize Pool
Gas Costs
Match-6 Winners
Hours since Prior Draw
CAKE Price
Blockchain Transactions (Millions)

Mean
6,257
4.989
170,835
0.634
0.003
17.09
11.496
6.397

SD
3,562
0.18
77,866
0.166
0.053
9.792
6.67
2.994

Min
1,311
4.034
41,676
0.329
2.669
2.595

Max
21,665
5.886
455,174
1.126
26.134
16.263

N

Empirical Specification
We estimate the variable relationships using two complementary modeling strategies on

wallet-level Tickets Sold. In the first strategy, we estimate a linear two-stage instrumental

variable (IV) estimator for panel data model (2SLS) using the xtivreg2 command in Stata

(Schaffer, 2020). The first-difference transformation removes time-invariant unobserved effects,

while the IV approach addresses potential endogeneity of the ticket Total Cost and the Prize

Pool, which may be influenced by reverse causality or unobserved factors correlated with Tickets

Sold. We use robust standard errors to account for heteroskedasticity. First-stage regression

results are examined to assess the strength of the instruments.

To complement the first-difference IV models, we also estimate analogous control

function Poisson models, following the methodology proposed by Lin and Wooldridge (2019).

These models account for the count nature of ticket sales data, which may exhibit overdispersion

or non-linear relationships not fully captured by the linear first-difference models. The control

function approach similarly addresses endogeneity by incorporating the residuals from the first-

stage regressions into the Poisson framework, providing a robustness check on our primary IV

results. This dual estimation strategy allows us to evaluate the consistency of our findings across

different modeling assumptions, enhancing the reliability of our inferences about the

determinants of lottery ticket sales.

The endogenous variables are instrumented using three variables: (1) the difference of the

CAKE token price from draw number n and draw number n + 1 (d,-./ ); (2) the number of

Binance Smart Chain transactions (Blockchain Transactions) in millions on the day of the draw,

and (3) the injected amount of CAKE to the draw (Bonus CAKE) in millions of USD.

The fluctuation of the CAKE token price between draws has a direct, externally-driven

effect on the lottery system. Although the ticket price is fixed at a value equivalent to $5 USD

right after one draw ends, the amount of USD required to meet this CAKE-denominated ticket

price changes during the intervening period to the next draw. Fluctuations in the CAKE price can

reasonably be viewed as exogenous over this short period, as it is impacted by macro impacts in

the cryptocurrency markets and short-term trading or transactions that are largely unrelated to

short-term lottery activity. For context, the largest amount of draw sales during our study period

was $107,446, while the largest volume day for CAKE tokens during the period was roughly

$1.74 billion (CoinGecko, 2025).

Blockchain Transactions also serves as an instrument for Total Cost, as higher network

activity on the Binance Smart Chain increases gas prices, which directly increases the gas cost

component of Price (BNB Chain Blog, 2024). This network activity is driven by broader usage

of the Binance Smart Chain ecosystem and is exogenous to specific lottery-related activities.

Given the scale of CAKE token trading volumes and BSC network activity relative to lottery

sales, these instruments are unlikely to be influenced by the lottery dynamics, supporting their

validity in addressing endogeneity in our models.

Bonus CAKE has an exogenous impact on Prize Pool, as it is set by the lottery operators

and is unrelated to the individual ticket sales or participant behavior within a given draw,

ensuring its independence from the endogenous variation in prize amounts. Its impact should

therefore entirely be transmitted through the Prize Pool variable.

2SLS Model

In the first stage, the first-differenced endogenous variables are regressed on the first-

differenced values of all exogenous variables. Let i index the individual or wallet and t index

time (draw). The prefix Δ denotes the first difference operator.

ΔTotal Cost#'

= 𝛾0 + 𝛾+ Δ𝛿CAKE,#' + 𝛾2 ΔBSC transactions#' + 𝛾3 ΔBonus CAKE#' + 𝛾45 Δ𝑋#' + Δ𝑢+#'

ΔPrize Pool#'

= 𝛽0 + 𝛽+ Δ𝛿CAKE,#' + 𝛽2 ΔBSC transactions#' + 𝛽3 ΔBonus CAKE#' + 𝛽45 Δ𝑋#' + Δ𝑢2#'

(1)

(2)

In the second stage, the first-differenced dependent variable (Tickets Sold) is regressed

on the predicted first-differenced endogenous variables from the first stage, and the first-

differenced values of the other exogenous variables.

ΔTickets Sold#'

E
E6' + 𝛿2 ΔPP
G6' (3)
= 𝛿+ ΔTicket E
Total Cost6' + 𝛿2 ΔPrize
Pool6' + 𝛿35 Δ𝑋#' + 𝜁#' ΔTS#' = 𝛿+ ΔTTC

Control Function Model

First, we model the endogenous variables as linear functions of all strictly exogenous

variables and wallet-specific fixed effects. The exogenous variables include the vector of

controls 𝑿𝒊𝒕 and the instruments. These reduced form equations are estimated using linear fixed-

effects regression in StataMP 15 (StataCorp, 2017):

Total Cost#'
= 𝛼,# + 𝛾+ 𝛿,-./,' + 𝛾2 BSC transactions' + 𝛾3 Bonus CAKE' + 𝑿𝒊𝒕 𝛄5𝟒 + 𝑢#',,:('

(4)

Prize Pool#'
= 𝛼;# + 𝛽+ 𝛿,-./,' + 𝛽2 BSC transactions' + 𝛽3 Bonus CAKE' + 𝑿𝒊𝒕 𝜷5𝟒 + 𝑢#',;::<

(5)

The dependent variable, Tickets Sold is modeled in the second stage using a Poisson distribution.

The expected value of Tickets Sold, conditional on the explanatory variables and the first-stage

residuals, is modeled using a log link function. Where ci is the multiplicative wallet-specific

fixed effect handled by the estimator, (θ) are the structural coefficients of interest, and (ρ) are the

coefficients on the control functions used to test for endogeneity. Bootstrapped standard errors

are estimated using 300 replications.

𝐸(Tickets Sold#' | … , 𝑐# )
E
= 𝑐# expT𝜃Cost Total Cost#' + 𝜃Pool Prize Pool#' + 𝑋#' 𝜃= + 𝜌Cost 𝑢̈ E
6',,:(' + 𝜌Pool 𝑢̈ 6',;::< W

(6)

Results

The first-stage results for the estimated 2SLS models are described in Table 2. The results

are empirically consistent with our hypothesized relationships. The first-stage regressions

establish the relationship between the endogenous variables (Total Cost and Prize Pool) and the

instrumental variables, including CAKE Price Change, Blockchain Transactions, and Bonus

CAKE. For Total Cost, both hypothesized instruments predict the endogenous variable,

including CAKE Price Change (β = 0.263, p < 0.001) and Blockchain Transactions (β = 0.014, p

< 0.001). Bonus CAKE shows a significant effect on Prize Pool (β = 0.859, p < 0.001).

Instrument validity is further supported by weak identification and overidentification

tests. The Cragg-Donald Wald F-statistic (68018.29) far exceeds the Stock-Yogo critical values

(e.g., 13.43 for 10% maximal IV size), rejecting the null hypothesis of weak identification and

confirming that the instruments are sufficiently strong to identify the endogenous variables. The

Hansen J statistic for overidentification (Hansen J = 0.671, χ²(1), p = 0.4128) fails to reject the

null hypothesis, supporting the exogeneity of the instruments and suggesting that CAKE Price

Change, Bonus CAKE, and Blockchain Transactions are uncorrelated with the second-stage error

term.

Table 2: First-Stage Results - First Difference Regressions

CAKE Price Change
Bonus CAKE
Blockchain Transactions
Hours since Prior Draw
Lag Match-6 Winner

(1)
2SLS

(2)
2SLS

(3)
Control
Function

(4)
Control
Function

Total Cost
0.263***
(0.001)
0.133***
(0.003)
0.014***
(0.001)
0.00002***
(0.000003)
-0.418***
(0.004)

Prize Pool
0.004***
(0.000)
0.742***
(0.001)
-0.000*
(0.000)
-0.0004***
(0.00003)
-0.038***
(0.001)

Total Cost
0.264***
(0.0005)
0.281***
(0.004)
0.022***
(0.0001)
0.0008***
(0.00003)
-0.332***
(0.004)

Prize Pool
0.003***
(0.0001)
0.859***
(0.001)
-0.003***
(0.00003)
-0.0006***
(0.000008)
-0.050***
(0.001)

Second Lottery
Constant

Weekday Indicator
Observations

0.034***
(0.001)
-0.002***
(0.000)
Yes***
346,928

0.009***
(0.000)
-0.001***
(0.000)
Yes***
346,928

-0.059***
(0.001)
5.504***
(0.001)
Yes***
847,087

0.038***
(0.0003)
0.162***
(0.0003)
Yes***
847,087

First-stage regression for Price, Prize (USD, m) and Expected Value. Robust standard errors in parentheses. *
p<0.05, ** p<0.01, *** p<0.001

In the second-stage regressions (Table 3), we estimate the number of tickets purchased

using both first-difference instrumental variable and conditional fixed-effects Poisson models

with a control function approach to address endogeneity. In the 2SLS model, a $1 increase in the

ticket costs is related to roughly one-half tickets purchased on average (β = -0.540, p < 0.001),

and a $1 million increase in Prizes is associated with 8.16 more tickets purchased on average (β

= 8.161, p < 0.001), indicating sensitivity to nominal price and strong responsiveness to jackpot

size. The presence of a Lag Match-6 Winner increases ticket purchases by roughly three quarters

of a ticket (β = 0.742, p = 0.005) but only two instances were recorded of jackpot winners, so

these estimates are unreliable. Hours since Prior Draw has a small positive effect (β = 0.011, p <

0.001), while the Second Lottery is not significant (β = 0.605, p > 0.05).

Table 2: Main Results - Panel data models with possibly endogenous regressors
(1)
(2)
2SLS
Control Function
Total Cost
-0.540***
-0.086***
(0.132)
(0.021)
***
Prize Pool (Millions)
8.161
1.339***
(0.295)
(0.048)
***
Hours since Prior Draw
0.011
.00002
(0.001)
(.0003)
Lag Match-6 Winner
0.742**
0.159***
(0.263)
(.040)
Second Lottery
0.605
-0.077***
(0.632)
(0.011)
Control Function Prices
0.082**
(0.024)
Control Function Prizes
-0.205**
(0.069)

Constant
Weekday Indicator

Observations
Unique Wallets

-0.513***
(0.018)
Yes
346,928
53,367

Yes
755,756
83,711

Robust standard errors in parentheses. * p<0.05, ** p<0.01, *** p<0.001

In the Poisson model, a $1 million increase in Prize Pool is associated with a 133.94%

increase in ticket purchases (β = 1.339, 95% CI [1.246, 1.433], p < 0.001), which given the

average number of tickets purchased in the estimation sample (m = 4.686), equates to roughly

6.27 more tickets sold per wallet. A $1 increase in Total Costs reduces ticket purchases by 8.63%

(β = -0.086, 95% CI [-0.127, -0.046], p < 0.001), which equates to 0.40 fewer tickets purchased

based on wallet averages. Both these effect sizes are similar in magnitude to the linear 2SLS

model estimates. Lag Match-6 Winner increases ticket purchases by 15.92% (β = 0.159, 95% CI

[0.080, 0.238], p < 0.001), while Second Lottery reduces ticket purchases by 7.65% (β = -0.077,

95% CI [-0.099, -0.054], p < 0.001). Hours since Prior Draw is not significant (β = 0.00002, p >

0.05). The control function residuals for Total Costs (β = 0.082, p < 0.01) and Prizes (β = -0.205,

p < 0.01) are significant, further confirming endogeneity.

General Discussion

Recent advancements in blockchain scalability (Thibault et al., 2022) created

opportunities for more complex product designs, transcending the basic mechanics of first-

generation gambling products (Scholten et al., 2020). Today's consumers can engage with

numerous on-chain games, such as lotteries, table games, slot machines, and sports betting. As

blockchain-facilitated gambling grows, the need to understand consumer behavior on these

platforms increases. Blockchains could potentially improve the user experience but could also

disrupt a significant revenue source for public services while contributing to public health risks

associated with gambling harm (Ariyabuddhiphongs, 2011; Egliston & Carter, 2023).

This study investigated consumer behavior in a novel context: a large-scale lottery

operating entirely on a public blockchain. By leveraging granular wallet-level transaction data

and employing a dual estimation strategy to address endogeneity, we examined the impact of

jackpot size, ticket cost, and prior winner effects on lottery participation. Our findings largely

indicate that, despite the technological novelty and unregulated nature of the environment,

consumer behavior in this crypto-lottery mirrors patterns well-documented in traditional,

regulated lottery markets.

Consistent with our first hypothesis (H1) and a vast body of traditional lottery literature,

we found a strong positive relationship between the Prize Pool size and Tickets Sold per wallet.

This suggests the allure of large, potentially life-changing jackpots, potentially driven by

preferences for skewness or specific utility curve considerations, remains a strong motivator for

participation, even within a digital cryptocurrency-based environment. This quantitative result

was corroborated by our qualitative content analysis of user discussions on Telegram, where

interest in jackpot size was the most prominent theme.

Our second hypothesis (H2), predicting a negative relationship between cost and

participation, was also supported. Both the linear and Poisson models indicated that higher Total

Cost (incorporating both the nominal ticket price and variable gas fees in USD equivalent)

significantly reduced the number of tickets purchased. This finding is particularly noteworthy

because estimating nominal price elasticity in traditional lotteries is often hampered by a lack of

price variation. The unique dynamics of this crypto-lottery, where a ticket price fixed

momentarily in CAKE tokens translates to a variable amount of volatile USD, combined with

fluctuating network gas fees, provided the necessary variation to identify this effect. The content

analysis further supported this finding, revealing user awareness and discussion around both

ticket price and gas costs, indicating that participants are sensitive to the overall cost outlay, not

just the potential prize.

Finally, we found some evidence consistent with the 'halo effect' observed in traditional

lotteries (H3) but we had insufficient occurrences of jackpots to view these effects as reliable.

The presence of a Lag Match-6 Winner was associated with increased ticket sales in the

subsequent draw in both models. This occurred despite the absence of traditional media coverage

or specific 'lucky store' effects, potentially driven instead by community discussion (as seen in

the content analysis) and the inherent transparency of winner information on the blockchain.

Phenomena linked to cognitive biases like the representativeness heuristic may persist in this on-

chain environment, but more data will be needed to confirm the estimate's reliability.

Methodologically, the consistency between the linear first-difference 2SLS model and the

fixed-effect Poisson control function model strengthens confidence in our findings. The

significance of the control function residuals in the Poisson model confirmed the presence of

endogeneity related to Total Cost and Prize Pool, validating the necessity of our IV strategy.

Furthermore, the use of wallet-level panel data, a level of granularity rarely available in lottery

research, represents a significant methodological advancement enabled by blockchain's

transparency.

Theoretical and Practical Implications

From a theoretical perspective, our results suggest that established models of lottery

consumer behavior that are rooted in entertainment value, cognitive biases, and specific utility

functions appear largely transferable to this new technological domain. The prominence of

jackpot seeking over explicit expected value calculations, both in our models and user

discussions, aligns with prior work suggesting heuristics and framing effects are likely drivers of

lottery demand. This study serves as an important empirical bridge between traditional gambling

research and the emerging field of decentralized finance and blockchain consumer behavior.

For policymakers and regulators, the study underscores that despite operating in an

unregulated, pseudonymous, and technologically distinct environment, crypto-lotteries elicit

consumer behaviors similar to those seen in regulated markets. This implies that concerns

regarding consumer protection, gambling disorders, and the potential social costs associated with

traditional lotteries may extend to their blockchain counterparts. While blockchain offers

potential tools for transparency and auditing, the borderless and often pseudonymous nature

presents unique regulatory challenges.

Limitations and Future Research

This study, while offering novel insights, has several limitations. First, our analysis is

confined to a single platform and product, PancakeSwap Lottery V2. Findings may not

generalize to other crypto-lotteries or different blockchain ecosystems. Second, while wallet-

level data is granular, a wallet address does not necessarily equate to a unique individual, as

users can manage multiple wallets. Third, the content analysis, while insightful, was limited to

the platform's main English Telegram channel over a specific three-month period and may not

represent the full spectrum of user opinions or behaviors. Fourth, the limited number of jackpot

winners during the study period impacts the robustness of the halo effect finding.

More broadly, while many lottery studies focus on demand elasticity relative to expected

value, directly modeling the impact of expected value presented significant empirical challenges

in this product design. Since the prizes were a scalar multiple of the Prize Pool, expected value

was largely determined by changes in the Prize Pool and Ticket Cost. The inherent endogeneity

in prize sharing (based on total tickets sold influencing individual payout per winner)

complicates the identification strategy for EV itself. Given these challenges, and qualitative

findings suggesting users focus more on primary components like jackpot size and cost, our

study deliberately focused its endogeneity correction on Prize Pool and Total Cost. This

represents a limitation in terms of directly measuring EV elasticity as commonly formulated in

the literature, though it allowed for robust estimation of the effects of its key underlying drivers.

Future research could expand on these findings in several directions. Replicating the

analysis on other onchain gambling platforms would test the generalizability of these behavioral

patterns. Investigating player heterogeneity, such as distinguishing between casual participants

and heavy users, could reveal different sensitivities to price and jackpots. Methodological

advancements in linking wallets or modeling multi-wallet usage would enhance the precision of

individual-level analyses. Likewise, longitudinal studies tracking wallets over longer periods

could provide valuable data on the potential development of problematic risk-taking behaviors in

this environment. Some scholars argue that blockchain-enabled gambling is evident in digital

asset speculation (Delfabbro et al., 2021; Philander, 2023; Steinmetz, 2023), which may have

entrenched a specific culture of risk-taking in this onchain economy. Finally, comparative studies

analyzing user behavior across regulated fiat lotteries and unregulated crypto-lotteries could

further illuminate the specific impact of the blockchain context and regulatory environment.

Conclusion

This study demonstrates that core drivers of traditional lottery demand persist strongly

within a major blockchain-based lottery. By utilizing the unique data transparency of blockchain

and advanced econometric techniques to address endogeneity, we provide robust evidence

supporting these relationships at the individual wallet level. These findings contribute to both the

gambling studies literature and the understanding of consumer behavior in nascent blockchain

ecosystems, highlighting implications for platform design, theoretical models, and regulatory

considerations in this rapidly evolving space.

Data availability
Study data is available at: https://osf.io/4gn87/?view_only=9d5ef53efe5a457cb1f590143dccd14f

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Running head: ONCHAIN LOTTERY

Appendix A: Lottery Draw Variable Correlations

Variable

Tickets
Sold

Expected
Value

Ticket
Price

Prizes

Gas
Costs

Match-6
Winners

CAKE
Price

Blockchain
Transactions
(Millions)

0.014
0.012

Hours
since
Prior
Draw
-0.158
0.517

Tickets Sold
Expected Value

1.000
0.394

0.394
1.000

0.016
-0.004

0.905
0.548

0.309
0.032

0.683
-0.179

0.408
-0.084

Ticket Price

0.016

-0.004

1.000

0.048

0.005

-0.050

0.028

0.027

-0.034

Prizes
Gas Costs

0.905
0.309

0.548
0.032

0.048
0.005

1.000
0.407

0.407
1.000

0.018
0.046

-0.143
-0.335

0.622
0.500

0.419
0.687

Match-6 Winners

0.014

0.012

-0.050

0.018

0.046

1.000

-0.027

0.000

0.027

Hours since Prior Draw
CAKE Price

-0.158
0.683

0.517
-0.179

0.028
0.027

-0.143
0.622

-0.335
0.500

-0.027
0.000

1.000
-0.493

-0.493
1.000

-0.384
0.565

Blockchain Transactions
(Millions)

0.408

-0.084

-0.034

0.419

0.687

0.027

-0.384

0.565

1.000