The Kelly Criterion in C#

Given a bank roll, a stake you have already bet and a potential pot of winnings, the Kelly Criterion should calculate for you the optimal amount you should bet to maximize your winnings in the long run.

• http://en.wikipedia.org/wiki/Kelly_criterion

So, here’s what looks like a trivial piece of code, but is actually quite powerful:

public class KellyEvaluator
{
private decimal proportion;
public KellyEvaluator(decimal proportion = 1.0M)
{
this.proportion = proportion;
}

public decimal MaxBankRoll(decimal bankRoll, decimal pot, decimal stake, decimal ourWinPercentage)
{
return bankRoll * MaxFraction(bankRoll, pot, stake, ourWinPercentage);
}

//given our current bankroll, a pot, an amount we’ve already staked, 
//our win percentage and the mean for the # of players,
//what is the maximum value we should allow ourselves to bet?
public decimal MaxNormalisedBankRoll(decimal bankRoll, decimal pot, decimal stake,
decimal ourWinPercentage, decimal meanWinPercentage)
{
return bankRoll * 
MaxNormalisedFraction(bankRoll, pot, stake, ourWinPercentage, meanWinPercentage);
}

//given a win% and an amount we’ve already staked, whatis the max we can bet
public decimal MaxNormalisedFraction(decimal bankRoll, decimal pot, decimal totalStaked,
decimal ourWinPercentage, decimal meanWinPercentage)
{
decimal f = 0.0M;
decimal proposedBet = bankRoll;
decimal max = 0.0M;
while (proposedBet > 0.0M)
{
f = NormalisedFraction
(bankRoll, pot – totalStaked, proposedBet, ourWinPercentage, meanWinPercentage);
if (f >= 0.0M)
max = f;
proposedBet -= 1.0M;
}

return max;
}

//given a win% whatis the max we can bet
public decimal MaxFraction
(decimal bankRoll, decimal pot, decimal totalStaked, decimal ourWinPercentage)
{
decimal f = 0.0M;
decimal proposedBet = bankRoll;
decimal max = 0.0M;
while(proposedBet > 0.0M)
{
f = Fraction(bankRoll, pot – totalStaked, proposedBet, ourWinPercentage);
if (f >= 0.0M)
max = f;
proposedBet -= 1.0M;
}

return max;
}

private decimal NormalisedFraction(decimal bankRoll, decimal potentialWinnings, decimal ourStake,
decimal ourWinPercentage, decimal meanWinPercentage)
{
decimal delta = ourWinPercentage – meanWinPercentage;
decimal edgePercentage = delta / meanWinPercentage;

return Fraction(bankRoll, potentialWinnings, ourStake, edgePercentage);
}

private decimal Fraction(decimal bankRoll, decimal potentialWinnings, 
                         decimal ourStake, decimal ourWinPercentage)
{

//b:1 i.e., if pot is 100 and call value is 20 and we’ve staked nothing else so far, then 5:1
decimal b = potentialWinnings / (ourStake);
decimal f = ((b * ourWinPercentage) – (1 – ourWinPercentage)) / b;

return f * proportion;
}
}