I will be writing about sports betting here, not casino games. Let's discuss what the optimal bet size is depending on the profit expectation. Most likely, different strategies allow different percentage values of a single bet as a percentage of the entire bankroll. You often see the opinion that the size of a single bet should be from 1 to 5%. This is a logical opinion, but I came across an interesting argument that quite logically justifies lower bets.
To put it briefly, the point of very small bets is to not lose the bankroll in the worst-case scenario. Let's say the effectiveness of your strategy is 60%. That is, for every 100 bets you will have 60 winning and 40 losing ones.
1. It is logical that these bets will be fixed in size.
2. At the very beginning, the size of this fixed bet will be approximately 1/1000 of the bankroll.
3. 60 winning bets should significantly exceed the size of 40 losing ones.
The thing is that average values are characterized by dispersion. And if on average you have 60 winning bets out of 100, this does not mean that within each hundred bets you will have exactly 60 winning ones. It may well be that at the very beginning the ratio will be different. And you will come to the ratio of 60/40 only with a very large number of played bets (about 1000).
Here is what the author writes about this in the book "How to beat the line of the handicap"
It may help you to stay in the game if you imagine a cigar box that contains 1000 tickets with sports bets - 575 winning and 425 losing. Your task will be to pull out one of the coupons, write down in a notebook whether you won or lost, put the ticket back in the box, shake it and repeat the process. This is analogous to waiting for a win equal to 57.5 percent. Common sense dictates that you should eventually win more than you lose, all the time, given enough observations. After all, every time you stick your hand in the box, you have 575 chances of getting a winning ticket and 425 chances of getting a losing ticket. The problem is how many winning tickets you will get over the next ten or twenty bets, and that is, in the grand scheme of things, just guessing. You will probably get more wins than you lose, but there are no guarantees. Those 425 tickets can really hurt. You can very well end up with an incredible number of losses, even after playing for a long time. However, given enough attempts, you will eventually win. Your main goal is to make sure that you can predict more winners than losers with some accuracy. In other words, you should keep your bet sizes small enough in relation to your bankroll so that a losing streak doesn't "kill" your bankroll and force you to stop betting as a business.