Dice

Chance and 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%