// IN EDITING
Title: Analysis of reward mechanism for quizmarket
Author: Noorul H. Ali (computer science and engineering), Indian Institute of Information Technology Vadodara, Gujarat, India
Correspondence: 201851078@iiitvadodara.ac.in
Abstract
Introduction
Results
Discussion
Methods
References
Appendix
A reward algorithm is needed for games which rewards risk, i.e. early play, and extends the longevity of a reward pool. This would allow a higher number of players and greater engagement. I created a reward mechanism that rewards risk, lasts longer, and is more profitable than existing mechanisms. I also implemented an algorithm within the mechanism to self-correct in outlier performance. This reward mechanism was used in TURBLAZE, a mobile game designed for high school students. The game has quizzes. Gamers pay a fixed fee to participate in a quiz and win a reward if their score is above a certain threshold.
This algorithm was designed specifically with a mobile game in mind. TURBLAZE is a mobile game I designed to increase student participation in curriculum by making a mobile video game for high school education. Quizmarket is a marketplace in this game for quizzes, where details such as reward, participation fee, difficulty level, reward history etc. are shown to the gamer.
Each quiz has a fixed prize pool which is to be distributed appropriately to winners. The reward mechanism we have made is such that the number of winners is maximized, while maintaining hierarchy in winners. Hierarchy is such that being early is rewarded. The quiz also has to ensure that all expenses incurred, including prize pool and hosting expenses, are less than the money made from the fee. The mechanism takes into account all kinds of expenses and delivers a way to host a profitable quiz while maximizing the number of participants. It is also fair to all participants.
Existing reward mechanisms for games
Other games that have reward mechanisms use randomness to create fairness in gambling. Examples of these include fantasy sports games [1], online rummy [2], and betting sites [3]. Pre-set probabilities ensure that the game makes money. This simplifies the game significantly, as randomness within range introduces luck, which works in favor for these games. These games are not just about skill, and their algorithms reflect that. But we need knowledge to be source of rewards,
and believe luck should not deter a knowledgeable person.
Algorithms in casinos
A normal odd-even betting game in which getting an even
number is a win and an odd number is a loss has a probability
of 50-50. Roulette adds two numbers into the losing pile
and shifts the probability slightly to ensure the casino always
makes money. Almost all games are ultimately designed to
make the casino a profit, when the game is played at scale.
Casinos build their foundations on luck. It is always the
element of randomness and luck that makes it money. From
small village gambles ( satta) to large casinos in Vegas, games
are always rigged to make the house money. We are inspired
by these algorithms but the randomness of a dice roll too often
overpowers skill.
C. Blockchain gambling pools
Betting pools have emerged on blockchain technology [4]–
[6]. These bets are made with many people in a pool, and upon
completion of bet condition, a winner is chosen at random.
There is an inherent lack of instant personal feedback, due to
randomized distribution of prize.
Bitcoin reward for each mined block halves roughly every
4 years, when a particular number of blocks is mined. This
ensures that the overall supply of bitcoin tokens remains fixed
at 21,000,000. Inspiration is taken from this infinite geometric
progression, because prize pool for every quiz is also fixed.
III. P ROBLEM FORMULATION
Each game is a 10 minute quiz. Score above threshold, win
reward. Else, get online resources to learn what you got wrong.
Each quiz has a fixed prize pool (pp). This is initial capital.
The reward (r) for winners comes from this pool. This pool
is distributed in such a way that numbers of winners are
maximized and early winners score more. Number of winners
is directly proportional to number of registrations, and hence
directly proportional to profitability of quiz.
A. Constants
Registration fee (f) is constant. This is the fee that a user
gambles on and pays to participate in quiz. This used to
make quiz profitable, all expenses are less than the total fee
collected.
Cost/user (c): this is the cost incurred per game per user.
Registration, cloud expenses, etc. are included in this. It is
formulated as a fixed percentage of prize pool.
Hosting cost (h): this is company expenses for hosting
quiz, formulating questions etc. Also formulated as a fixed
percentage of prize pool
Initial prize pool (ipp): This is the total prize pool allotted
to quiz before it starts. It is fixed and rewards are subtracted
from it. Its use needs to be maximized.
B. V ariables
Threshold (t): every quiz has a winning score. If a student
scores above this score, they win the reward. This is variable
so that the difficulty of quiz varies as per the performance of
gamers.
Prize pool (pp): this is the prize pool left after subtracting
rewards.
Cost-percentage (cp): this is the percentage of registration
fee kept by game. This is used to meet expenses and make
quiz profitable. It is variable according to the party hosting
the quiz. A higher percentage allows quicker cost recovery
but limits the number of winners, hence longevity of quiz.
Reward(r): this is the reward given to a user upon scoring
higher than the threshold. It is variable such that risk taking
of early winners is rewarded. This is deducted from prize pool
(pp).
C. Core Ideas
• Threshold depends on success rate and existing prize
pool, so that more difficult quizzes are incentivized
• Prize pool varies as registrations increase, since a per-
centage of fee goes to pool. This means cp less than 1.
• Reward must be based on success rate and current prize
pool
• Quiz is viable only till reward greater than fee
IV. P ROPOSED SOLUTION
A. Case 1 algorithm: Limited case with simple GP
Prize pool (pp) is assumed to be constant. Cp=100%, the
entire registration fee (f) of every user is taken by quiz as
expense. Upon winning,
pp = pp–r (1)
Follows GP for reward, sum of rewards = prize pool
Rewards : a, ar, ar2. . . arn (2)
Reward(nth) = arn (3)
n → inf inity (4)
For r = 0.9695, n is maximum while r (reward) greater than f
(fee)
n = 37 (5)
B. Limitations of case 1 algorithm
Constant prize pool limits number of winners. This is
problematic since longevity and consequent profitability of
quiz is affected.
C. Case 2 algorithm: optimized GP
Prize pool (pp) is assumed to be variable. Cp = 75%.
Thus 25% of f (registration fee) is added to prize pool to
increase longevity. 75% of f (fee) is taken as expense. For
every registration,
pp = pp + 0.25f (6)
Upon winning,
pp = pp–r (7)
In geometric progression of reward
pp = a(1 − xn)/1 − x (8)
Constant = pp (9)
V ariables = x, n (10)
Result:
n = 46 (11)
Changing cp increases the maximum number of winners by
24%, allowing a comfortable profitability ratio for standard
20% win-ratio.
D. Limitations of case 2 algorithm
Algorithm does not modify itself to account for everyone
winning, can lead to losses
E. Case 3 algorithm: self optimizing GP
This builds on case 2 algorithm. Threshold (t) corrects
itself based on success rate. A quiz with too many winners
has a higher threshold, becoming more difficult to win, and
effectively decreasing the number of winners to maintain the
pre-set win-ratio.
Initial threshold is t 0, which is the standard pre-set thresh-
old that is to be maintained. t is the updated threshold, which
updates itself after every 5 quiz completions. For a 70%
success ratio,
t 0 = 0 .7 (12)
Correcting factor (cf):
cf = (1/5 − s)sf (13)
1/5 = 0.2 = average success rate needed
s = success rate, changes after every 5 quiz completions
sf = perturbation rate (scaling factor)
For sf = 10,
t = 10(1/5 − s) + 70 (14)
Threshold lies between 60% and 95%
Case 3 algorithm varies difficulty within reasonable limits
to account for all types of users, ensuring game keeps making
money
V. I NTERPRETATIONS
A. Basic assumptions
If ipp is set to $100, with f = $1 for every user,
B. Case 1 results
cp = 100%, all of f (fee) is taken as expense. The maximum
number of winners achieved in this case is 37. For a 20%
success ratio, this allows for 185 registrations.
C. Case 2 results
cp = 75%, $0.75 of f (fee) is taken as expense. $0.25 is
added to pp on each registration. The maximum number of
winners achieved in this case is 46. This is a 24% increase.
For a 20% success ratio, this allows for 250 registrations.
These winners must be interspersed to allow 250 registrations.
In case they occur together, the prize pool will get exhausted
quickly.
D. Case 3 results
In this, threshold optimizes itself to ensure scalability. It
maintains 46 winners no matter how they occur in registra-
tions. Winners need not be interspersed. Ensures profitability
at scale (20 gamers to 20000 gamers).
VI. E XPERIMENTAL DISCUSSIONS
Scalability of this algorithm has been tested. It works
to generate rewards in appropriate geometric progressions,
from 20 users to 20000. Various tools to generate backend
infrastructure were discussed upon.
VII. F URTHER DEVELOPMENTS
This reward mechanism can be used in any kind of
task/game where there is a limited resources have to be
effectively distributed on the basis of a certain parameter like
skill. Using this, the architecture for mobile game TURBLAZE
was created.
VIII. C ONCLUSIONS
Inspired from casinos and Bitcoin [4], [7], rewards are
a geometric progression that ensures maximum number of
winners for a particular pool. This allows for maximum
utilization of pool, while reward is profitable compared to
registration fee. The reward also fluctuates on the basis of
success rate of quiz (which determines quiz difficulty in real-
time). Finally, in the spirit of casinos, the game is always
rigged to make TURBLAZE money. No matter the number
of winners, the quiz difficulty and innate (by design) structure
that fluctuates reward on the basis of success rate, ensures
profitability at every scale, from 20 players to 20000.
IX. T HANKS
I am extremely grateful to Pratik Shah sir for listening
patiently as I rambled on and on about far off goals, while I
delayed my submissions. Thank you for the clarity and giving
me insights. They helped me a lot. The discussions with you
were extremely fruitful and helped me achieve important goals
I was unaware of. I used to only write code, but this internship
taught me what it means to make a project, and I am very
thankful for that. Thank you once again sir.
REFERENCES
[1] “Dream11 website: Simplistic fantasy sports gambling
game.” (), [Online]. Available: https : / / www. dream11 .
com/.
[2] “Teen patti website: Card game gambling.” (), [Online].
Available: https://www.teenpatti.co.in/.
[3] “Bet365 website: Online betting website.” (), [Online].
Available: https://www.bet365.com.
[4] S. Nakamoto, “Bitcoin: A peer-to-peer electronic cash
system,” Bitcoin.org, 2008. [Online]. Available: https://
bitcoin.org/bitcoin.pdf.
[5] V . Buterin. “A next-generation smart contract and de-
centralized application platform,” Ethereum Foundation.
(2013), [Online]. Available: https : / / ethereum . org / en /
whitepaper/ (visited on 04/28/2023).
[6] “Kryptium website: Blockchain betting pool website.” (),
[Online]. Available: https://kryptium.io/.
[7] J. Matonis, “Bitzino and the dawn of ’provably fair’
casino gaming,” F orbes Magazine, 2012. [Online]. Avail-
able: https://www.forbes.com/sites/jonmatonis/2012/08/
31/%20bitzino-and-the-dawn-of-provably-fair-casino-
gaming/?sh=6d31601e7593.