I'll do one (assuming an adverse edge of 2.7%), you do the other (no edge) . . .

For a thousand spins, betting one unit per spin (on an even-payoff bet), the EV for losing spins will be 1000 x 19/37 (=~514), and the EV for winning spins must threfore be 1,000 less this figure (486). To calculate the variance / standard deviation, one uses:

SQRT ( number of trials x probability x (1-prob) ). So the standard deviation for the number of losing spins is:

SQRT ( 1,000 x 19/37 x (1-19/37) ) = 15.81. 3 x Std Devs would therefore be 47.43.

The worst case scenario for betting 1,000 spins on an evens-payoff bet would therefore be 561 losing spins (514+47). Three StdDevs either side of the EV covers 99.73% of outcomes, so there is a relatively tiny amount of room for worse results than this.

So assuming the worst case scenario is losing 561 units, and therefore winning 439 units, there's the potential to end up with a net loss of 122 units. So having a bankroll of 122 units would mean you'd have only a 0.14% chance of tapping out (only half of the 0.27 not covered by 3 x Std Devs as the other half would be at the "winning" side of the bell curve.

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Repeating the exercise with 1 x standard deviation . . .

1 x Std Dev south of the EV would be 530 losses (514+16) - so losing 530 units, and therefore winning 470 units, the net loss would be 60 units. 1 Std Dev either side of the EV covers 68.26% of occurances, and so the half south of the EV (losing side) covers 34.13%. Having a bankroll of 60 units would therefore leave you with a risk of tapping out of 15.87% (50.00%-34.13%).

Two standard deviations covers 95.44% of occurances, so half of this - 47.72% - that is south of the EV, gives a risk of tapping out of 2.28% (50%-47.72%).

I found this useful tool on the web which allows you to see what multiples of the standard deviation any particular percentage of occurances is covered by, ie 0.5 Std Devs either side equates to 38.30% of the population. Very handy for us degenerate gamblers.

https://www.mathsisfun.com/data/standard-normal-distribution-table.html [nofollow]=====================================================

This is a fairly simple set of calculations, but once you start introducing progressions, inconsistent betting patterns and similar, it becomes a lot more complicated, and a degree of over-estimating can save on the aspirin. I apologise if this comes across as patronising in any way - it's not intended to.

Best of luck at the felt.