I regular listen the Business of Betting Podcast, when driving to work. There I stumbled over a episode, where a experiment with a 60/40 coin was discussed. People were provided a modified coin, which shows head with a probability of 60%. Knowing this fact they should choose a stake, which they think maximizes their profit, and flip the coin 100 times. The result of this experiment was really surprising: Despite a positive edge many people gone busted. But why did this happen?
This answer is pretty simple: They carelessly chose their staking size with the intent to maximize the profit. At a first sight this sounds logical. When you got an edge, you will make profit over long term. And the higher your stake per coin flip, the higher will be your overall profit. This is shown by the first picture. During the experiment the participants got a starting bank of 100 units and should flip the coin 100 times. The graphs show one possible progress for these 100 coin flips for 5 different stake sizes. The stake size of 50€, which is equates 50% of the starting bank, provides by far the highest.
But everyone, who chooses such high stakes, misses, how probabilities work. Even with a winning probability of 60%, their could be several consecutively tails, which would eat up your bank. To respect this, we have to know, which losing streak we could expect during 100 coin flips.
Following formula can be used to calculate the longest expected winning and losing streaks:
n represents the number of trails and P represents the probability for a win or a loss. Applied to our coin flipping problem: There could be a series of 5 tails and a series of 9 heads during the experiment. With a stake size of 50€ such a tails streak corresponds a loss of 250€. So there is a risk of getting busted, if such a streaks occurs before the bank has grown a bit. Exactly this happened in the simulation shown at the second picture. A losing streak started at the 8th flip. A person with a stake of 50€ would have gone broken after 14 flips. All other staking plans survived the losing streak.
But respecting the longest expected losing streak before setting your staking size is just the first step. Facing 5 tails in a row is definitely unlucky. But when betting with money things of course can get even more unlucky. Just image you first face 5 tails, 1 head and after that 4 tails. This would even equal a loss of 400€ with a 50€ staking size. And this is exactly what happened in the 3rd simulation example. After 100 flips again all staking plans end with a profit. But during this sequence of 100 flips, tails occurred so often, that only the 5€ staking plan would have saved you to not go bankrupt. The probability for such a unlucky series may be small. But we are speaking of probabilities. Everything is possible.
This example shows, that it is not only necessary to respect the length of the maximum losing streak. To get an estimation for your staking, you also have to consider a risk factor for longer “unlucky” phases, especially at the beginning, when your bank is not yet big enough to absorb such losses.
Following formula can be used to calculate your needed starting bank or the best stake size:
The Blog, where I found this formula suggests a risk factor of 5. This means your starting bank should be around 5 times of your longest expected losing streak. Following table shows the suggested starting bank for the different stake sizes and different risk factors.
It is surprising to see, how big the starting bank for the experiment should be, if you choose a stake size of 50€. Calculated the other way around, the optimal stake size for the given starting bank would have been 4€, which may seem very small in comparison to the given edge of a 60/40 coin.
So what does this experiment tells an ambitious or professional sports bettor? Of course the first goal of a sports bettor should be to find a predictive model or betting system, which provides an edge against the bookmaker. But even, if a bettor found some edge, he or she have to think about a wise staking method. Otherwise you could go busted, even with the biggest edge.
If you have further questions, feel free to leave a comment or contact me @Mo_Nbg.
References:
[1] Soccerwidow, The science of calculating winning and loosing strikes, 2016, https://www.soccerwidow.com/football-gambling/betting-knowledge/value-betting-academy/learning-centre/betting-terminology/science-calculating-winning-losing-streaks/
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