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import { Fraction } from "./Fraction";
import { OutcomeFunction } from "./OutcomeFunction";
import { Token, TokenEffects } from "./tokens";
import {
allCombinations,
arrayEquals,
cartesianProduct,
combinations,
factorial,
flatten,
replace
} from "./utils";
interface PullWithOdds {
tokens: Token[];
odds: Fraction;
}
export type OddsFn = (
numTokensPulled: number,
bag: Bag,
outcomes: TokenEffects,
outcomeFunction: OutcomeFunction
) => number;
/**
* Compute the odds of a particular combination of tokens based on how many
* tokens are not "redraw" tokens.
* It took me a lot of time to get this formula right. Many thanks to those who
* helped me get it.
*
* @param {number} totalNumberOfTokens
* The total number of tokens in the bag
* @param {number} numberOfTokensInCombination
* The number of tokens in the combination
* @param {number} numberOfNonRedrawTokensInCombination
* The number of tokens in this combination that are not "redraw" tokens
* @return {number}
* The odds of this combination
*/
function oddsOfCombination(
totalNumberOfTokens: number,
numberOfTokensInCombination: number,
numberOfNonRedrawTokensInCombination: number
): Fraction {
return new Fraction(
factorial(totalNumberOfTokens - numberOfTokensInCombination) *
factorial(numberOfTokensInCombination - 1) *
numberOfNonRedrawTokensInCombination,
factorial(totalNumberOfTokens)
);
}
/**
* Return all possible sets of n tokens that can be pulled from the bag along
* with the odds of pullingthis particular set among all possible sets.
* For exemple, if drawing only 1 token from a bag containing only a +1 token
* and 2 -1 token, the result will be:
* * +1 with a 0.33 odds
* * -1 with a 0.66 odds
*
* @param {number} numTokensPulled
* The number of tokens simultaneously pulled from the bag.
* @param {Bag} bag
* The bag from which the tokens are pulled.
* @param {TokenEffects} outcomes
* The token effects if needed (which is true if some of them have redraw effects).
* @return {PullWithOdds[]}
* The list of possible pulls along with their odds as fractions.
*/
function getPossiblePullsWithOdds(
numTokensPulled: number,
bag: Bag,
outcomes?: TokenEffects
): PullWithOdds[] {
let allPossibleCombinations: Token[][] = [];
if (outcomes) {
const tokensWithRedraw = bag
.getTokens()
.filter(t => outcomes.getEffect(t).isRedraw());
const tokensWithoutRedraw = bag
.getTokens()
.filter(t => !outcomes.getEffect(t).isRedraw());
const combinationsOfRedrawTokens = allCombinations(tokensWithRedraw);
const combinationsOfNonRedrawTokens = combinations(
numTokensPulled,
tokensWithoutRedraw
);
allPossibleCombinations = cartesianProduct(
combinationsOfRedrawTokens,
combinationsOfNonRedrawTokens
).map(c => flatten(c));
} else {
allPossibleCombinations = combinations(numTokensPulled, bag.getTokens());
}
const allCombinationsWithOdds: PullWithOdds[] = allPossibleCombinations.map(
tokens => ({
odds: oddsOfCombination(
bag.getTokens().length,
tokens.length,
outcomes
? tokens.filter(token => !outcomes.getEffect(token).isRedraw()).length
: tokens.length
),
tokens: tokens.sort()
})
);
return allCombinationsWithOdds.reduce(
(reducedCombinations: PullWithOdds[], currentCombination: PullWithOdds) => {
if (reducedCombinations.length === 0) {
return [currentCombination];
} else {
// Find a combination with the same set of tokens
const matchingCombinationIndex = reducedCombinations.findIndex(
({ tokens }) => arrayEquals(tokens, currentCombination.tokens)
);
if (matchingCombinationIndex > -1) {
// Update the existing combination by adding the odds
const updatedCombination = {
odds: reducedCombinations[matchingCombinationIndex].odds.add(
currentCombination.odds
),
tokens: reducedCombinations[matchingCombinationIndex].tokens
};
return replace(
reducedCombinations,
matchingCombinationIndex,
updatedCombination
);
} else {
// Add the combination
return [...reducedCombinations, currentCombination];
}
}
},
[]
);
}
/**
* Return all possible sets of n tokens that can be pulled from the bag along
* with the odds of pullingthis particular set among all possible sets.
* For exemple, if drawing only 1 token from a bag containing only a +1 token
* and 2 -1 token, the result will be:
* * +1 with a 0.33 odds
* * -1 with a 0.66 odds
*
* @param {number} numTokensPulled
* The number of tokens simultaneously pulled from the bag.
* @param {Bag} bag
* The bag from which the tokens are pulled.
* @param {TokenEffects} outcomes
* The token effects if needed (which is true if some of them have redraw effects).
* @return {{ tokens: Token[]; odds: number }[]}
* The list of possible pulls along with their odds.
*/
export function drawFromBag(
numTokensPulled: number,
bag: Bag,
outcomes?: TokenEffects
): { tokens: Token[]; odds: number }[] {
return getPossiblePullsWithOdds(numTokensPulled, bag, outcomes).map(
pullWithOdds => ({
odds: pullWithOdds.odds.valueOf(),
tokens: pullWithOdds.tokens
})
);
}
/**
* Compute the odds of a particular outcome when pulling tokens from the bag.
*
* The outcome function is called for each possible combination of `numTokens`
* from the bag and return `true` or `false` wether this specific combination
* is a success or not. This function is called with first argument being the
* combination (it will contain exactly `numTokens` tokens), second optional
* argument being the effects of the tokens and third optional argument being
* the Chaos bag.
*
* The simplest outcome function is checking if a particular token was pulled:
*
* ```javascript
* function pulledASkull(tokensPulled) {
* return tokensPulled[0] === ArkhamOdds.Token.SKULL;
* }
* ```
*
* Using the token effects mapping, you can check if the skill test is a
* success when the total skil vallue is 2 above the difficulty.
*
* ```javascript
* function isSuccessWhenTwoAbove(tokensPulled, tokenEffects) {
* return tokenEffects.isSuccess(tokensPulled, 2);
* }
* ```
*
* @param {number} numTokensPulled
* The number of tokens simultaneously pulled from the bag.
* @param {Bag} bag
* The bag from which the tokens are pulled.
* @param {TokenEffects} outcomes
* The token effects.
* @param {OutcomeFunction} outcomeFunction
* The outcome function returning `true` if the pulled tokens represent a
* desired outcome and `false` otherwise.
* The first argument passed to the function are the tokens pulled, the second
* is the token effects map and the third is the bag.
* The outcome function should always assume that redraw tokens are counted
* and that pulled tokens contains the result of redrawing.
* @return {number}
* The odds of the desired outcome.
*/
export const odds: OddsFn = (
numTokensPulled: number,
bag: Bag,
outcomes: TokenEffects,
outcomeFunction: OutcomeFunction
): number => {
const possiblePullsWithOdds = getPossiblePullsWithOdds(
numTokensPulled,
bag,
outcomes
);
const filterCondition = (possiblePullWithOdds: PullWithOdds) => {
return outcomeFunction(possiblePullWithOdds.tokens, outcomes, bag);
};
return possiblePullsWithOdds
.filter(filterCondition)
.reduce(
(totalOdds, successfulPullWithOdds) =>
totalOdds.add(successfulPullWithOdds.odds),
new Fraction(0, 1)
)
.valueOf();
};
/**
* Similar to `odds` but this time putting tokens back into the bag between
* each pull.
*
* It should be used for abilities like Wendy's:
*
* ```javascript
* let wendyOdds = ArkhamOdds.oddsWithRedraw(
* 2, theBag, theEffects,
* ArkhamOdds.successChoosingBest(0));
* ```
*
* TODO Update this function to account for tokens with a redraw effect.
*
* @param {number} numTokensPulled
* The number of tokens sequentially pulled from the bag while putting them
* back in between each pull..
* @param {Bag} bag
* The bag from which the tokens are pulled.
* @param {OutcomeFunction} outcomeFunction
* The outcome function returning `true` if the pulled tokens represent a
* desired outcome and `false` otherwise.
* The first argument passed to the function are the tokens pulled, the second
* is the token effects map and the third is the bag.
* @return {number}
* The odds of the desired outcome.
*/
export const oddsWithRedraw: OddsFn = (
numTokensPulled: number,
bag: Bag,
outcomes: TokenEffects,
outcomeFunction: OutcomeFunction
): number => {
const comb: Token[][] = cartesianProduct(
...Array(numTokensPulled).fill(bag.getTokens())
);
const filterCondition = (tokensPulled: Token[]) => {
return outcomeFunction(tokensPulled, outcomes, bag);
};
return comb.filter(filterCondition).length / comb.length;
};
export * from "./bag";
export * from "./cards";
export * from "./tokens";
export * from "./OutcomeFunction";
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