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]. Preset 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.
Blockchain gambling pools
Betting pools have emerged on blockchain technology [4,5,6]. 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.
Each game is a 10 minute quiz. Players scoring above the threshold win rewards. Players scoring below the threshold are given online educational resources on their wrong answers. Each quiz has a fixed prize pool (pp), the initial capital. The reward (r) for winners comes from this pool. Optimizing the game means distributing the pool to maximize the numbers of winners and reward earlier players more than later ones. The number of winners is directly proportional to the number of registrations for a game, and hence directly proportional to the game's profitability.
Constants
1. Registration fee (f): Constant fee a player pays to participate in a game. Generates profit for the game. Cumulative expenses for the game are less than the total fee collected.
2. Cost/player (c): C incurred per game per user. Registration fees included here. It is taken as a fixed percentage of the prize pool (pp).
3. Hosting cost (h): Expense for hosting a game, including making questions, ensuring game fairness etc. It is also taken as a fixed percentage of the prize pool (pp).
4. Initial prize pool (ipp): Total prize pool allocated to a game before it starts. It is fixed and rewards are subtracted from it. The goal is to maximize the number of players playing in this fixed prize pool.
Variables
1. Threshold (t): Every game has a threshold winning score. If a player scores above this, they win the reward. Threshold is variable to modulate the difficulty of the game according to the remaining prize pool, or the performance of gamers who played the game.
2. Prize pool (pp): Remaining prize pool left after subtracting rewards of winning players
3. Cost-percentage (cp): Fraction of registration fee kept by the game, not added to the prize pool. It is used for expenses and profits. Higher percentage makes for faster cost recovery but limits the number of winners, hence longevity of the game. (1-cp)*f is added to prize pool after each registration, contributing to longevity of the game.
4. Reward (r): Reward for winning players scoring above the threshold. It is variable to encourage risk, rewarding early winners more than late winners. It is deducted from the prize pool (pp).
5. Success rate (s): Number of winners / Number of total players. This metric is regularly updated after n game runs (5 below).
Core ideas for reward algorithm
1. Threshold depends on success rate and existing prize pool, incentivizing games of higher difficulty.
2. Prize pool varies as registrations increase as a percentage of registration fee (f) adds to the prize pool (pp). Thus, cp < 1.
3. Reward depends on success rate (fraction of winners) and current prize pool.
4. Game is viable for players till reward > fee.
Case 1 algorithm: Limited case with simple GP
Constant prize pool (pp) assumption. cp = 1 ,entire registration fee (f) of every player is taken by game. Upon winning:
Geometric progression (GP) for rewards:
Reward for nth player:
Assuming n (number of players) tends to infinity, r is calculated with the constraint that reward at each step is greater than fee f
Number of winners in limited case with simple GP reward algorithm (n):
37 winners in 100 prize pool. The limitations of simple GP reward algorithm is that a constant prize pool limits the number of winners. This affects longevity and consequent profitability of the game.
Case 2 algorithm: Optimized GP
Variable prize pool (pp) and cp = 0.75. 25% of each registration fee (f) added to the game's prize pool to increase its longevity. 75% of f used for expenses. For every registration:
Upon winning:
Prize pool (pp) is sum of reward geometric progression:
Number of winners in Optimized GP reward algorithm (n):
Optimized GP reward algorithm changes cost-percentage to use a portion of registration fees as prize pool. This small change increases the number of possible winners by 24%. The game is profitable with 20% win-ratio (20% winners).
The major limitations of Optimized GP reward algorithm is that the algorithm does not modify itself to account for many winners. Since the game is skill-based and not luck-based, it is entirely possible that a game only has winners. In this case, Optimized GP reward algorithm leads to loss for the game host.
Case 3 algorithm: Self-optimizing GP reward algorithm
This builds on Optimized GP reward algorithm with a self-correcting threshold (t). The threshold (t) corrects itself based on success rate. A game with too many winners has higher threshold (t), becoming more difficult to win, and effectively decreasing the number of winners to maintain a preset win-ratio.
Initial threshold (t0) is preset threshold to be maintained. t is updated threshold, which updates itself after every 5 game runs. For example, in a game with 20% preset win-ratio and 70% threshold:
Correcting factor (cf) is added to the threshold after every 5 game runs. This changes the threshold. Correcting factor depends on current success rate (s), calculated after every 5 game runs, and a scaling factor (sf). Assuming win-ratio of 0.2 (20% winners) and base threshold of 0.7 (game won at scoring > 70%):
For sf = 10, threshold is changed after every 5 game runs by this equation:
Threshold lying between 60% and 95% is optimal for players. Self optimizing GP reward algorithm varies difficulty within reasonable limits to account for all types of players and ensures the game runs long and profitably.
Assuming initial prize pool (ipp) = 100, f = 1 for each new player
1. Simple GP reward algorithm
Cost percentage (cp) = 100%, all of fee (f) used for expenses. The maximum number of winners under Simple GP reward algorithm is 37. For a 20% success/win ratio, this allows 185 registrations.
2. Optimized GP reward algorithm
Cost percentage (cp) = 75%, 0.75 of fee (f) used for expenses. 0.25 added to prize pool (pp) for each player registration. The maximum number of winners under Optimized GP reward algorithm is 46, 24% increase over Simple GP reward algorithm. For a 20% success ratio, this allows almost 250 registrations. Winners must be interspersed for 250 registrations. In case they occur together, the prize pool will be exhausted quickly, closing the game early.
3. Self-optimizing GP reward algorithm
In this, the threshold optimizes itself to ensure scalability. It maintains 46 winners no matter the order of winners in registrations. Winners need not be interspersed. Self-optimizing GP reward algorithm ensures profitability at scale (20 to 20000 gamers). Scalability of Self-optimizing GP reward algorithm has been tested to generate rewards in appropriate geometric progressions from 20 to 20000 players.
This reward mechanism can be used in any kind of task/game where there are limited resources to be effectively distributed on the basis of parameters like skill, intelligence or hardcoded metrics. Using this, the architecture for mobile game (TURBLAZE) was made. Inspired by casinos and Bitcoin [4,7], rewards are a geometric progression to ensures maximum number of winners for a particular pool. This utilizes the prize pool to the maximum. Rewards also fluctuate on the basis of the game's success rate, determining quiz difficulty in real-time for quizzes app (TURBLAZE). Finally, in the spirit of casinos, the game is always rigged to make the game host money, even under skill-based conditions. No matter the number of winners, the game's difficulty and innate structure that fluctuates reward on the basis of success rate, ensures profitability at every scale, from 20 to 20000 players.
I am extremely grateful to Pratik Shah sir for listening patiently. Thank you for helpful clarity and insights. Discussions with you helped me achieve important goals I was unaware of.
[1]: Fantasy sports game. Website. Link
[2]: Card game gambling. Website. Link
[3]: Online betting website. Link
[4]: S. Nakamoto. Bitcoin: A peer-to-peer electronic cash system. Bitcoin.org. 2008. Link
[5]: V . Buterin. A next-generation smart contract and decentralized application platform. Ethereum Foundation. 2013 Link
[6]: Blockchain betting pool. Website. Link.
[7]: J. Matonis. Bitzino and the dawn of provably fair casino gaming. Forbes Magazine. 2012. Link