Saturday, October 4, 2014

Optimized Betting for Multiple Games at the Same Time

Update: My new site, Snoozle Sports, has a tool that does these calculations for you.

Based on the 2007 paper, Algorithms of Optimal Allocation of Bets on Many Simultaneous Events by Chris Whitrow, the Kelly criterion for the bets should be used for multiple simultaneous bets (like betting on football games that are playing at the same time) when the number of bets is small. In other words you should use the Kelly bets for instances where the total percentage of the bets is not near your whole bank roll. As you number of bets increases, and the sum of the bets approaches 100% of your bankroll you should bet the percent of the better's edge.

The better's edge is your probably of getting the bet right minus the book probability which is measured as the 1 / (book odds + 1). For instance, in a college football game where I predict I have a 60% probability of being right and the house had 100/110 odds on game, the book probability would be 1/(100/110 + 1) = 0.524. The better's edge in this instance would be 0.60 – 0.524 = 0.076 or 7.6%. So, I would be 7.6% of my bankroll on the game.

Also, according to Whitrow's computer models for optimal performance if the percentage of bets is greater than 100% of your bankroll scale the bets so they are under your bankroll limit based on the better's edge.

This conclusion from the paper is based on empirical evidence and not theory where the author did not know why this observation was happening. The empirical evidence and model was convincing, and I will use this system for my bets.

How will it work in practice

For simplicity, let us say I have $1000 in my bankroll for the picks for October 3, 2014 and October 4, 2014.

On October 3, my prediction algorithm picked 2 games with an advantageous probabilities:
  • Syracuse +2.5 vs Louisville at a 75% probability of being correct with a 48% Kelly criterion
  • San Diego State +3.0 at Fresno State at a 54.55% probability of being correct with a 5% Kelly criterion
By adding up the Kelly bets, 48% + 5% = 53%, the total bet of the payroll does not get close to 100% of my bankroll, so according to the paper's author Kelly betting is optimal.

On October 4, my prediction algorithm picks 20 games where I have an advantage, where the sum of the probabilities,
.48+.48+.40+.33+.33+.27+.25+.19+.17+.16+.1+.1+.08+.06+.05+.04+.03+.03+.02+.01=3.58 or 358%, obviously, I cannot bet over 100% of my bankroll. For this situation, the author's paper concludes that the optimal would be percentage of the bankroll approximately the better's edge. So, using the better's edge as the percent of bankroll to bet is advised. 

Given the better's edge values from October 4,
.23+.23+.19+.16+.16+.14+.13+.12+.09+.08+.08+.05+.05+.04+.03+.02+.01+.01+.01 = 1.83 or 183% of bankroll which is still not possible. The author then recommends scaling the bets, so the values are less than 100% of bankroll or if you want to be more conservative less than the percent of bankroll you want to bet at a given time. I am comfortable betting on all the bets recommended by the algorithm due to the very low probability they will all be wrong. The scaled bets would become
0.12 0.12 0.10 0.08 0.08 0.07 0.07 0.06 0.04 0.04 0.04 0.02 0.02 0.01 0.01 0.01
respectively for the first 14 games, and I will drop off the ones below 1%. Using this metric my total betting of my bankroll would be 88%.

This is system I tried for this Friday and Saturday of Week 6, I have not modeled it my algorithm yet, but I thought I would take a leap of faith, and model it later.


  1. I really enjoyed reading your article. I found this as an informative and interesting post, so I think it is very useful and knowledgeable. I would like to thank you for the effort you have made in writing this article.

  2. This post is on Algorithms based sports by Dr.Wag`s Picks.He has Optimized Betting and Horse Racing Odds for Multiple Games at the Same Time.Thanks for an interesting post keep sharing more info related it.

  3. For +2.5 decimal odds (1.5-1 fractional odds), with 0.75 probability, does not the Kelly criterion yield (1.5*0.75 - 0.25)/1.5 = 0.58 ?

    Where does the 0.48 come from?

    1. I was assuming -110 in US odds, or a 0.91 return a winning bet and +2.5 was the against the spread line. Where the equation would be ((0.91 * .75) - 0.25)/0.91. which would be .475.

    2. This comment has been removed by the author.

  4. This comment has been removed by a blog administrator.

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