The Probability of Halving Your Bankroll With the Kelly Criterion

Posted by Ryan

If you’re not familiar with the Kelly criterion then I suggest you read my money management guide before proceeding.

Up until recently I used a 50% Kelly fraction when sizing my bets. I did this because I thought that 50% of full Kelly was good enough to reduce my volatility yet still make a good profit.

That changed, however, once I got a better grasp of the risk associated with betting various fractions of the Kelly criterion. It all started when I read the Kelly FAQ at BJMath.com.

The FAQ suggests you look at the probability of doubling your bankroll before losing half of it as a guide to choosing the Kelly fraction that fits you best. Seeing the numbers (the table from Q9) encouraged me to run simulations in regards to sports betting to see how these probabilities fit my expectations.

The table below shows the results:

Note: the Probability column denotes the probability of halving ones bankroll before doubling it when using the listed Kelly Fraction.

Kelly Fraction	Probability	Median Bets to Double	Min Bets to Double	Max Bets to Double
100%	32.69%	138	15	1427
90%	29.19%	163	18	1422
80%	25.54%	205	18	1916
70%	20.70%	254	29	2502
60%	15.66%	321	35	2695
50%	11.04%	418	43	3797
40%	5.15%	558	69	5042
30%	1.90%	788	111	6550
20%	0.28%	1210	229	8208
10%	< 0.01%	2466	704	9397

The simulations used to calculate the data in the table above assume an event with a 55% chance of winning against odds of -110.

As you can see from the table above, a larger Kelly fraction greatly increases the risk to halving your bankroll before doubling it.

The world isn’t perfect, and it takes a really long time to have full Kelly be superior to other options. As such, I’ve chosen to scale back to a roughly 33% betting fraction to fit my risk profile better.

You should be using the Kelly criterion

If you’re not doing so already, you should be using the Kelly criterion to size your wagers. Read my money management guide and pick the appropriate Kelly fraction from the table above and start profiting.