Optimizing Bet Sizes with the Kelly Criterion

Remember a few weeks back when we discussed stock market investing using the Kelly Criterion to determine asset allocations? Today we’re going to go in a different direction and use Kelly for what it was intended – betting!

The Kelly Criterion is a formula you can use to determine the proper size of a bet when there are known odds and a definite payout.  With a little hand waving and some basic math (as I proved a few weeks back), you can also use it to help guide your investment decisions – namely when determining the size of a position you should take.  Let’s hop into some calculators.

Kelly Criterion Input
Input Data Values
Probability – Enter your odds of winning, say, ‘.5′ for a coin flip, or ‘.1′ for one number out of 10.
Odds – Enter your net odds received, say ’2′ for 2 to 1 odds.
Bankroll – Enter the amount of money you have to bet. (Dollars)
Adjusted Kelly – Enter Your ‘Kelly Adjustment’ to divide. ’1′ for full, ‘.5′ for Half-Kelly, ‘.25′ for Quarter-Kelly, etc.

Kelly Criterion Calculation
Calculated Results Values
Kelly Criterion (Adjusted)
Bet This Much (Adjusted)

Code created with assistance from Political Calculations

A Practical Application of Kelly To Betting Strategies

The calculator above comes prefilled with the simplest example – a game of coin flipping stacked in your favor. Roughly, your friend really wants to flip coins, and is willing to pay 2 to 1 on any bet you make. Your odds of winning any one flip are 50/50. So, your probability is .5… 50%. Your ‘odds offered’ are ’2 to 1′ so you enter 2. Bankroll is how much money you have to bet on these flips.

Hit calculate, and just as I explained on this podcast, you’ll see that you should definitely take the bet – for 25% of your bankroll.

Now, to find a friend stupid enough to offer those odds!

Of course, you can see practical the practical value of Kelly betting when it comes to things with discrete results and obvious probabilities – say pot odds in a poker hand. Your mileage may vary.

What do you think about simple Kelly betting? Even though it is designed to never let you go bankrupt, Kelly still allows wild volatility swings. Do you prefer another strategy? Perhaps half or quarter Kelly methods?

Comments

  1. says

    I just put in the criteria for basic craps betting…and I can’t imagine the amount of volatility I’ll have! The bet size is bigger than I expected.

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