# Provably Fair

Game events are translation of the randomly generated floats into a relatable outcome that is game specific. This includes anything from the outcome of a dice roll to the order of the cards in a deck, or even the location of every bomb in a game of mines.

Below is a detailed explanation as to how we translate floats into events for each particular different game on our platform.

## Blackjack, Hilo & Baccarat

In a standard deck of cards, there are 52 unique possible outcomes. When it comes to playing Blackjack, Hilo & Baccarat on our platform, we utilise an unlimited amount of decks when generating the game event, and therefore each turn of a card always has the same probability. To calculate this, we multiply each randomly generated float by 52, and then translate that result into a particular card, based on the following index:

```
// Index of 0 to 51 : ♦2 to ♣A
const CARDS = [
♦2, ♥2, ♠2, ♣2, ♦3, ♥3, ♠3, ♣3, ♦4, ♥4,
♠4, ♣4, ♦5, ♥5, ♠5, ♣5, ♦6, ♥6, ♠6, ♣6,
♦7, ♥7, ♠7, ♣7, ♦8, ♥8, ♠8, ♣8, ♦9, ♥9,
♠9, ♣9, ♦10, ♥10, ♠10, ♣10, ♦J, ♥J, ♠J,
♣J, ♦Q, ♥Q, ♠Q, ♣Q, ♦K, ♥K, ♠K, ♣K, ♦A,
♥A, ♠A, ♣A
];
// Game event translation
const card = CARDS[Math.floor(float * 52)];
```

The only differentiating factor involved with these games is that with **Hilo**
and **Blackjack** there is a curser of 13 to generate 52 possible game events for
cases where a large amount of cards are required to be dealt to the player, whereas when it
comes to **Baccarat** we only ever need 6 game events generated to cover the most amount
of playable cards possible.

## Diamond Poker

When playing Diamond Poker, there is 7 possible outcomes in the form of gems. To achieve this, we multiply each float generated by 7 before it is translated into a corresponding gem using the following index:

```
// Index of 0 to 6 : green to blue
const GEMS = [ green, purple, yellow, red, cyan, orange, blue ];
// Game event translation
const gem = GEMS[Math.floor(float * 7)];
```

Both the dealer and the player are dealt 5 gems each, which means that a complete game of Diamond Poker requires the generation of 10 game events. The first 5 are assigned to the dealer and the second 5 are assigned to the player.

## Diamonds

When playing Diamonds, there is 7 possible outcomes in the form of gems. To achieve this, we multiply each float generated by 7 before it is translated into a corresponding gem using the following index:

```
// Index of 0 to 6 : green to blue
const GEMS = [ green, purple, yellow, red, cyan, orange, blue ];
// Game event translation
const gem = GEMS[Math.floor(float * 7)];
```

The player is then dealt 5 gems.

## Dice Roll

In our version of dice, we cover a possible roll spread of 00.00 to 100.00, which has a range of 10,001 possible outcomes. The game event translation is done by multiplying the float by number of possible outcomes and then dividing by 100 so that the resulting number fits the constraints of our stated dice range.

```
// Game event translation
const roll = (float * 10001) / 100;
```

## Limbo

When it comes to Limbo, we use a two-step process. Firstly, we take the float and multiply it by both the maximum possible multiplier and the house edge. Then, in order to generate a game event that has probability distribution , we divide the maximum possible multiplier by the result of the first step to create the game event in the form of a crash point.

```
// Game event translation with houseEdge of 0.99 (1%)
const floatPoint = 1e8 / (float * 1e8) * houseEdge;
// Crash point rounded down to required denominator
const crashPoint = Math.floor(floatPoint * 100) / 100;
// Consolidate all crash points below 1
const result = Math.max(crashPoint, 1);
```

## Plinko

For any game of Plinko, the generated outcome is based on the path of the falling ball. The game event determines the direction of the falling ball for each level in the falling process. Players can choose between 8 and 16 pins of play, which determines the number of game events required to generate a complete path from top to bottom. Since there are only two possible directions (left or right) the translation is done by multiplying each float by 2, which maps to the following index:

```
// Index of 0 to 1 : left to right
const DIRECTIONS = [ left, right ];
// Game event translation
const direction = CARDS[Math.floor(float * 2)];
```

## Roulette Roll

Our Roulette is derived from the European version of the game where the wheel consists of 37 possible different pockets, ranging from 0 to 36. The game event is calculated by multiplying the float by 37 and then translated into a corresponding pocket using the following index:

```
// Index of 0 to 36
const POCKETS = [
0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36 ];
// Game event translation
const pocket = POCKETS[Math.floor(float * 37)];
```

## Keno

Traditional Keno games require the selection of 10 possible game events in the form of hits on a board. To achieve this, we multiply each float by the number of possible unique squares that exist. Once a hit has been placed, it cannot be chosen again, which changes the pool size of the possible outcomes. This is done by subtracting the size of possible maximum outcomes by 1 for each iteration of game event result generated using the corresponding float provided, using the following index:

```
// Index of 0 to 39 : 1 to 40
const SQUARES = [
1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40 ];
const hit = SQUARES[Math.floor(float * 40)];
```

The fisher-yates shuffle implementation is utilised to prevent duplicate possible hits being generated.

## Mines

A mine game is generated with 24 separate game events, in the form of mines on the board. Each float is multiplied by the number of possible unique tiles still remaining on the board. This is done by subtracting the number of tiles remaining by 1 for each iteration of game event result generated using the corresponding float provided. The location of the mine is plotted using a grid position from left to right, top to bottom.

The fisher-yates shuffle implementation is utilised to prevent duplicate possible hits being generated. Between 1 and 24 game event results are used, based on the settings chosen.

## Video Poker

A video poker game involves 52 separate game events, in the form of cards in a deck. Each float is multiplied by the number of possible cards still remaining in the deck. This is done by subtracting the number of cards remaining by 1 for each iteration of game event result generated using the corresponding float provided. This is done by selecting a card from the following index:

```
// Index of 0 to 51 : ♦2 to ♣A
const CARDS = [
♦2, ♥2, ♠2, ♣2, ♦3, ♥3, ♠3, ♣3, ♦4, ♥4,
♠4, ♣4, ♦5, ♥5, ♠5, ♣5, ♦6, ♥6, ♠6, ♣6,
♦7, ♥7, ♠7, ♣7, ♦8, ♥8, ♠8, ♣8, ♦9, ♥9,
♠9, ♣9, ♦10, ♥10, ♠10, ♣10, ♦J, ♥J, ♠J,
♣J, ♦Q, ♥Q, ♠Q, ♣Q, ♦K, ♥K, ♠K, ♣K, ♦A,
♥A, ♠A, ♣A
];
// Game event translation
const card = CARDS[Math.floor(float * 52)];
```

The fisher-yates shuffle implementation is utilised to prevent duplicate cards being generated.

## Wheel

The game event number is calculated by multiplying the float by the possible outcomes in the segment. It is then used to determine the game event result as a multiplier, using the following index:

```
// Index per payout configuration
const PAYOUTS = {
'10': {
low: [ 1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0 ],
medium: [ 0, 1.9, 0, 1.5, 0, 2, 0, 1.5, 0, 3 ],
high: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 9.9 ]
},
'20': {
low: [
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0
],
medium: [
1.5, 0, 2, 0, 2, 0, 2, 0, 1.5, 0,
3, 0, 1.8, 0, 2, 0, 2, 0, 2, 0
],
high: [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 19.8
]
},
'30': {
low: [
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0
],
medium: [
1.5, 0, 1.5, 0, 2, 0, 1.5, 0, 2, 0,
2, 0, 1.5, 0, 3, 0, 1.5, 0, 2, 0,
2, 0, 1.7, 0, 4, 0, 1.5, 0, 2, 0
],
high: [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 29.7
]
},
'40': {
low: [
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0
],
medium: [
2, 0, 3, 0, 2, 0, 1.5, 0, 3, 0,
1.5, 0, 1.5, 0, 2, 0, 1.5, 0, 3, 0,
1.5, 0, 2, 0, 2, 0, 1.6, 0, 2, 0,
1.5, 0, 3, 0, 1.5, 0, 2, 0, 1.5, 0
],
high: [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 39.6
]
},
'50': {
low: [
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0,
1.5, 1.2, 1.2, 1.2, 0, 1.2, 1.2, 1.2, 1.2, 0
],
medium: [
2, 0, 1.5, 0, 2, 0, 1.5, 0, 3, 0,
1.5, 0, 1.5, 0, 2, 0, 1.5, 0, 3, 0,
1.5, 0, 2, 0, 1.5, 0, 2, 0, 2, 0,
1.5, 0, 3, 0, 1.5, 0, 2, 0, 1.5, 0,
1.5, 0, 5, 0, 1.5, 0, 2, 0, 1.5, 0
],
high: [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 49.5
]
}
};
// Game event translation
const spin = PAYOUTS[segments][risk][float * segments];
```

## Crash

See the BitcoinTalk seeding thread to learn about how we utilise the salt hash based provable fairness modal for this particular game.

## Slide

See the BitcoinTalk seeding thread to learn about how we utilise the salt hash based provable fairness modal for this particular game.

## Scarab Spin

The game event number is calculated by multiplying the float by the possible outcomes in the reel. The first 4 reels have a length of 30 possible outcomes, whilst the last reel has 41. The game event determines the central stop position for each reel. This game consists of 5 game event numbers, until the case of a bonus round, where more are generated.

## Blue Samurai

Blue Samurai slots has 3 different types of spins. Regular, bonus and special.

For regular and bonus spins, 18 floats from 0 to 1 are generated from your hash. Unlike Scarab Spin slots, which has fixed reels, Samurai slots has dynamic reels, meaning each symbol is generated from the corresponding float that was assigned to it.

We use weighted random sampling to assign each float to its corresponding tile, in the same order, moving down the reels, from left to right. Each symbol has its own fixed probability / chance of appearing in any one tile, with the outer 2 reels having a different set of probabilities to the inner 3 reels. For a bit more information on how symbols are selected, see fitness proportionate selection algorithm to learn more.

Special spins are slightly different. For a start only 12 floats are taken from your hash, as the outer reels are disabled. Between each special spin, any samurai symbols stay in place for the remainder of the game, with the payout being the final count of samurais. This means that if you were to have for example 1 samurai stick in the first spin - we'd technically only need 11 floats for the subsequent spin. For the sake of simplicity in the probably fair model, we just generate 12 floats every time, and if the float that was allocated for a tile has a stuck samurai from a previous spin, then that float is not used at all.