Any rational person should realise that no staking plan can turn a negative expectation game into a winning one.

But it took me a long while before I proved to myself why bad staking plans can ruin positive expectation games.

First note that you have no control over luck so the best you can expect in the long run is average luck.

Consider a simple fair, even, binary game such as a coin toss.

Assume you bet 50% of your bank. So after each toss you bank multiplies by either 0.5 or 1.5.

With average luck you would have an equal number of wins and losses. Order is irrelevant.

So your most likely bank after 2 games is 0.5*1.5 = 0.75 * B (your original bank) .

For n games your bank would most likely decay to B * 0.75^(n/2) .


Now even if you were to get a 33% bonus ("edge") for winning, you would still not break even.

If you change the key parameters in this simple example you should get a feel for what your optimum bet to bank ratio should be for any winning edge.


Or instead you could look up the Kelly staking formula which gives you a similar approximate result. Trouble is Kelly derived it for an entirely different application, and using that won't help you understand what you're doing.