As is common in the field, the rationale behind our staking plan is the Kelly formula, which accounts for both the difference between bookies and modeled odds (the advantage we think we have on the bookies) and the probability of winning. The outcome from the Kelly formula is an estimate (f) of the fraction of our bank we should stake on a given bet to guarantee an optimum return on the long term. This in essence is what drives the stake when following the Kelly strategy: your bet size increases with both your chance of winning and the advantage you think you have on the bookies.
The Kelly Criterion formula is: (bp-q)/b
B = the Decimal odds -1
P = the probability of success
Q = the probability of failure (i.e. 1-p)
Using a coin as an example of Kelly Criterion staking, consider you are betting on a coin to land on heads at 2.00. However, the coin is biased and has a 52% chance of ending up on heads. In this case:
Q = 1-0.52 = 0.48
B = 2-1 = 1.
This works out at: (0.52x1 – 0.48) / 1 = 0.04. Therefore the Kelly Criterion would recommend you bet 4% of your bankroll.
The Kelly Criterion works very well when you know the exact probability of your bet (a coin landing on heads) but runs into issues when less precise odds (a hockey team winning a game). Overconfidence in one’s ability to know their precise odds can lead to over betting (betting too much) which will lead to long term loss. That is why we recommend people use a fractional Kelly Criterion, in our examples we use Half Kelly Criterion meaning we take our recommend bet size and divide it in half. Building off our coin flipping example, if we were using a Half Kelly Criterion we would bet 2% of our bankroll.
Kelly Criterion also works based on compounding our bankroll. Example:
Day 1 Bankroll: $1000
Day 1 Winnings: $20
Day 2 Bankroll: $1020
An issue with the Kelly Criterion is that it is not explicitly built to handle simultaneous bets (betting multiple games being played at the same time). There is research exploring how to properly allocate one’s bankroll for simultaneous bets see here, here and here. To handle simultaneous betting, we used the following Kelly Criterion based staking strategy:
If we have two bets on one day, one calling for a full kelly wager of 2.5% and another calling for a 2% wager then we would bet (1-.025)*(1-.02)*2.5% = 2.387% on the first wager and (1-.025)*(1-.02)*2% = 1.91% on the second wager.