Dice

The game of dice rules the crypto casinos due to its popularity. It's a simple game of chance where the betting mechanisms can be easily customized. If you move the bar to the left, the reward of the multiplier for winning your bet increases, at the expense of the winning probability. By moving the bar to the right, the opposite occurs: your winning probability increases, but the multiplier's reward in case of a victory decreases. Users can also adjust the multiplier and the probability of winning by typing the desired values into the designated box. It's clear that this game maintains its popularity due to its simplicity and the ability to personalize each betting strategy.

CHANCE & MULTIPLIER

Dice is a game where you roll over (or equal to) or under (or equal to) a number to win. Chance is chosen by the player (0.01%-98%). The multiplier is set so the return is always 0.99 compared to the win chance. Through a simple formula (with Chance ranging from 0.1 to 95) the multiplier for every chance input from the player can be calculated.

$$\text{Multiplier} = 0.99 \frac{100}{\text{Chance}}$$

The available multipliers can be found in the Dice contract where 10421 stands for the 1.0421x multiplier and 9900000 for the 990x multiplier:

if (!(multiplier >= 10421 && multiplier <= 9900000))

Here are some examples of specific outcomes:

Player outcome	Chance	Multiplier
Win	95% (highest)	1.0421x
Win	50%	1.98x
Win	49.5%	2x
Win	0.1% (lowest)	990x
Loss	0.1%-95%	0x

House Edge

The 1% house edge is taken when the win chance is being calculated, because 99000000000 is always being divided by the multiplier:

uint256 winChance = 99000000000 / game.multiplier;

When we take the 2x multiplier as an example, 99000000000/20000=4950000 leads to a 49.5% win chance. This is a 1% house edge (50.5-49.5). On a win or loss the average return is always 0.99.

Odds

The numbers above lead to the following odds for Dice:

Odds	Outcome
Decimal odds	0.99
Return to Player	99%
Probability odds	49.5%