If the goal is to avoid bankruptcy, then the probability needs to be interpreted differently. If you bet the house every time, you're guaranteed to go bankrupt

If the goal is to avoid bankruptcy, then the probability needs to be interpreted differently. If you bet the house every time, you're guaranteed to go bankrupt eventually. Suppose instead you bet half your money on an event of 50% probability. If you take 1:1 odds on this, then when you lose, your money is divided by 2, but when you win it is only multiplied by 1.5. Your money will tend to decrease over time. You need to pick odds 1:a such that 1+a/2=2 => a=2. We recover our regular betting odds by betting a smaller portion of our money. If we bet a portion 1/d of our money on an event of probability 1/p, we needs odds 1:a such that 1+a/d=(d/(d-1))^(p-1). For large enough d we get a=p-1, as we would expect. Assume again you're betting half your money each round, but take a probability of winning of 84%, as in the article. You should take that bet at 1:1.14 odds, much less than the recommended 1:5 odds.