kelly calculator for sports betting american odds

If the standard deviation is 1.15, then the variance is 1.15 2 = 1.3225. From my Game Comparison Guide, we see the standard deviation of blackjack is 1.15 (which can vary according to the both the rules and the count). Remember that variance is the square of standard deviation, which is listed for many games in my Game Comparison Guide.Įxample 1: A card counter perceives a 1% advantage at the given count. For example, if a bet had a 2% advantage, and a variance of 4, the gambler using 'full Kelly' would bet 0.02/4 = 0.5% of his bankroll on that event. Most gamblers use advantage/variance as an approximation, which is a very good estimator. However, for bets with more than one outcome, that can be hard to determine.

For bets with more than one possible outcome, the optimal Kelly wager is that which maximizes the log of the bankroll after the wager.

Betting half the Kelly amount, for example, reduces bankroll volatility by 50%, but growth by only 25%.įor simple bets that have only two outcomes, the optimal Kelly bet is the advantage divided by what the bet pays on a 'to one' basis. While this does lower expected growth, it also reduces bankroll volatility. What is more commonly seen is betting less than the full Kelly amount. Anything greater than double Kelly results in expected bankroll decline. Betting double Kelly results in zero expected growth. While betting more than Kelly will produce greater expected gains on a per-bet basis, the greater volatility causes long-term bankroll growth to decline compared to exact Kelly bet sizing. The Kelly bet amount is the optimal amount for maximizing the expected bankroll growth, for the gambler with average luck. Kelly betting also minimizes the expected number of bets required to double the bankroll, when bet sizing is always in proportion to the current bankroll. This product is maximized by Kelly betting. Then the expected bankroll growth per bet would be: Suppose also the player bets 1% of his bankroll every bet. The probability of a 2 or 12 is 1/36 each, of any even money win is 14/36 and of a loss is 20/36. A 3, 4, 9, 10, or 11 still pay 1 to 1 and every other total loses. For the gambler/investor with average luck bankroll and a fixed bet size, the expected bankroll growth after one bet is:įor example, suppose a casino ran a promotion in craps where the 2 paid 3 to 1 and the 12 paid 4 to 1. The same principle would work for any investment with an expectation of being profitable. The Kelly Criterion is a bet-sizing technique which balances both risk and reward for the advantage gambler. On this page The Kelly Criterion Introduction

Kelly calculator for sports betting american odds