Fair Dice Game
Introduction
The Fair Dice Gambling Concept is an innovative and entertaining betting system based on rolling one or two six-sided dice.
This concept offers players several betting options with a range of probabilities and payouts, while ensuring that the expected value (EV) for each bet is always equal to 1, making it a fair game for the players.
In this document, we will outline the betting options, probabilities, payouts, and expected values for both the single-dice and two-dice games, as well as provide tables for the various bet types available.
Single-Dice Game
In the single-dice game, players place bets on the outcome of rolling one six-sided die.
There are three main bet types: Number bets, Odd/Even bets, and Big/Small bets.
Number bets
Players can choose one, two, or three numbers between 1 and 6. The probability and payout depend on the number of selected numbers:
1 number: 1/6 probability, 6x payout, EV = 1
2 numbers: 2/6 probability, 3x payout, EV = 1
3 numbers: 3/6 probability, 2x payout, EV = 1
Odd/Even bets
Players can bet on whether the rolled number will be odd or even. The probability and payout for this bet type are:
Odd/Even: 3/6 probability, 2x payout, EV = 1
Big/Small bets
Players can bet on whether the rolled number will be big (4, 5, or 6) or small (1, 2, or 3). The probability and payout for this bet type are:
Big/Small: 3/6 probability, 2x payout, EV = 1
Two-Dice Game
In the two-dice game, players place bets on the outcome of rolling two six-sided dice, with the result being the sum of the two dice.
Similar to the single-dice game, there are three main bet types: Number bets, Odd/Even bets, and Big/Small bets.
Number bets
Players can choose one or multiple numbers between 2 and 12. The probability and payout depend on the number selected, as each sum has a different probability of being rolled:
2 or 12: 1/36 probability, 36x payout, EV = 1
3 or 11: 2/36 probability, 18x payout, EV = 1
4 or 10: 3/36 probability, 12x payout, EV = 1
5 or 9: 4/36 probability, 9x payout, EV = 1
6 or 8: 5/36 probability, 7.2x payout, EV = 1
7: 6/36 probability, 6x payout, EV = 1
In addition to the basic bet types, the two-dice game also offers Double, Triple, and Quadruple bet types, where players can bet on two, three, or four specific sums, respectively. The probabilities and payouts for these bet types vary based on the specific numbers chosen. To ensure the expected value is 1 for any combination of numbers, you should calculate the combined probability for the chosen numbers and set the payout accordingly.
Here are examples for each bet type with consecutive probability sums:
Quadruple
2, 3, 4, and 5: 10/36 probability, 3.6x payout, EV = 1
3, 4, 5, and 6: 14/36 probability, 2.5714x payout, EV = 1
4, 5, 6, and 7: 18/36 probability, 2x payout, EV = 1
... and so on. A user can choose up to 6 numbers.
Selecting up to 6 numbers would follow a similar process. The formula will be as follows for all bets
The only Example you will need to understand this whole game
If a quintuple (5 numbers) bet is made, (Example: 3, 4, 6, 9, 11). If any of those numbers are rolled, the user wins. The probability of this win is calculated as the sum of each of the numbers.
In our example,
1) Rolling a 3 has a 2/36 probability
2) Rolling a 4 has a 3/36 probability
3) Rolling a 6 has a 5/36 probability
4) Rolling a 9 has a 4/36 probability
5) Rolling a 11 has a 2/36 probability
Summing all the probabilities: 2/36 + 3/36 + 5/36 + 4/36 + 2/36 = 16/36
% chance win
The users chance to win is exactly 16/36 or 44.44%
Payout
Inversing this Fraction (36/16) will yield a fair payout of 2.25x.
How to determine if this is a fair bet?
Probability of winning (with any of the 5 numbers): 16/36 or 44.44% Probability of losing: 20/36 or 55.56%
Payout for winning: 2.25x Loss for losing: 1x (the bet amount)
Expected Value (EV) = (Probability of winning * Payout for winning) - (Probability of losing * Loss for losing) EV = (16/36 * 2.25) - (20/36 * 1) = 36/36 - 20/36 = 16/36 - 20/36 = 0
Since the EV is 0, this indicates that the game is fair, with no inherent advantage for the player or the house.
Odd/Even bets
Players can bet on whether the sum of the two dice will be odd or even. The probability and payout for this bet type are:
Probability of rolling an odd number: There are 18 possible outcomes for rolling an odd number (3, 5, 7, 9, 11) out of the total of 36 possible outcomes.
Summing the individual probabilities: 2/36+4/36+6/36+4/36+2/36=18/36
This translates to a 50% chance of winning, resulting in a 2x payout if the bet is won.
Probability of rolling an even number: There are also 18 possible outcomes for rolling an even number (2, 4, 6, 8, 10, 12) out of the total of 36 possible outcomes.
Summing the individual probabilities: 1/36+3/36+5/36+5/36+3/36+1/36=18/36
This translates to a 50% chance of winning, resulting in a 2x payout if the bet is won.
Big/Small bets
Players can bet on whether the sum of the two dice will be small (2-6) or big (7-12). The probability and payout for this bet type are:
Small: 15/36 probability, 2.4x payout, EV = 1
Big: 21/36 probability, 1.7143x payout, EV = 1
Taxation
In our Fair Dice Gambling Concept, we implement a 1.5% tax on winnings to support the platform's sustainability and reward NFT holders of the Degen LP platform. Additionally, we introduce a maximum bet system that is based on the platform's float, ensuring responsible gambling and the platform's financial stability. This section outlines the taxation process, the distribution of the taxed revenue between the platform's float and Degen LP NFT holders, and the maximum bet system.
Taxation on Winnings
To maintain the platform's financial stability and ensure long-term operations, a 1.5% tax will be applied to all winnings. This tax serves to generate revenue that can be utilized for the platform's development and benefit the Degen LP NFT holders, creating a mutually beneficial ecosystem for both the platform and its supporters.
Revenue Distribution
The taxed revenue generated from the 1.5% tax on winnings will be split evenly, with 50% allocated to the platform's float and 50% distributed among the NFT holders of the Degen LP platform. This revenue distribution system aims to accomplish the following objectives:
Float Support: Allocating 40% of the taxed revenue to the platform's float ensures that the platform remains financially stable and is able to cover potential losses, maintain operations, and develop new features and improvements over time.
Degen LP NFT Holder Rewards: The remaining 50% of the taxed revenue will be distributed among the NFT holders of the Degen LP platform. This revenue-sharing model serves as an incentive for users to invest in and hold Degen LP NFTs, as they will receive a share of the platform's earnings as a reward for their support.
Degen LP Team: 10% of the taxed revenue will go towards platform operations, maintenance and future upgradind.
Maximum Bet System
To encourage responsible gambling and ensure the platform's financial stability, we have implemented a maximum bet system that directly correlates with the platform's float. The maximum bet allowed for each player is determined by the current size of the float, with a ratio of 100:1 and adjustments made in increments of 100 USD.
For instance, if the float has 500 USD, the maximum bet for each player will be set at 5 USD. As the float increases, the maximum bet limit will be adjusted in line with the new float value.
For example, if the float grows to 600 USD, the maximum bet allowed per player will rise to 6 USD. These adjustments occur in 100 USD blocks, ensuring that the maximum bet limit remains proportional to the size of the float.
As more people participate in the games, the 1.5% tax on winnings helps maintain the house edge, enabling the float to continuously increase while simultaneously distributing dividends to NFT holders indefinitely. This system guarantees the platform's financial stability, rewards its NFT holders, and promotes responsible gambling practices among players.
The Fair Dice Gambling Concept presents a diverse array of betting options tailored to accommodate varying risk tolerances and gameplay preferences, all while maintaining a fair gaming environment with an expected value of 1 for every bet type.
By offering players an assortment of bet types in both single-dice and two-dice games, this concept has the potential to attract a broad spectrum of users, ultimately providing an immersive and enjoyable gambling experience.
Furthermore, the inclusion of a taxation and revenue distribution system, along with a maximum bet system, ensures the platform's financial stability, rewards the Degen LP NFT holders, and fosters responsible gambling practices.
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