I have been trying to work this out, no-one so far can help me.

I'm sure you can all see the relevance of this to roulette,

Q. With a fair coin, my opponent flips 50 times, & I call heads or tails.

It is fair odds, ie I get back 2xbet if I win, 0 if I lose.

The average outcome is 25 wins, 25 losses.

However, if I make the assumption that I will win at least 15 times, how do I proportion my bets to be ahead at the 15th win, whilst minimising bets?

Further, write an equation to illustrate this with e= expected wins, n= total flips.

I know e=15, n=50.

I think if c=expected wins at any point in the series, bet=1+(losses/c) works, but

it does not take into account n.

And unfortunately, when we are down to 1 expected win, we are betting all our losses +1.

So could anyone help with this please?