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## Session win %

What's the formula for % chance of winning (being in profit any amount) after x amount of hands?

Assume flat betting with a set player edge

Im guessing its probably somewhat similar to the n0 formula

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Originally Posted by blueman
What's the formula for % chance of winning (being in profit any amount) after x amount of hands?

Assume flat betting with a set player edge

Im guessing its probably somewhat similar to the n0 formula
See BJA3, p. 21 and Table 2.2 at the bottom of the page. Just need the win rate and s.d. for the game in question. Then apply formula as described in the page 21 text, near the end.

Don

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Originally Posted by DSchles
See BJA3, p. 21 and Table 2.2 at the bottom of the page. Just need the win rate and s.d. for the game in question. Then apply formula as described in the page 21 text, near the end.

Don
I dont have BJA3, can anyone help?

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Originally Posted by blueman
I dont have BJA3, can anyone help?
You should be profoundly ashamed of yourself!

Don

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Originally Posted by DSchles
You should be profoundly ashamed of yourself!

Don
Turns out i do have this book lol. Didnt realize it was 3rd edition

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Reading page 21 and not understanding any kind of formula to determine this.

It says "determine what % of the SD the corresponding expected return represents" then find the area under the curve to the left of this figure.

Can you explain this in a pure mathematical formula? Like, how do i even make a curve?

I have EV of game and SD, isnt this all i need in order to find % win after x hands?

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Originally Posted by blueman
Reading page 21 and not understanding any kind of formula to determine this.

It says "determine what % of the SD the corresponding expected return represents" then find the area under the curve to the left of this figure.

Can you explain this in a pure mathematical formula? Like, how do i even make a curve?

I have EV of game and SD, isnt this all i need in order to find % win after x hands?
...asking Don to explain in pure math formulas...prepare to be even more confused.

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## Example Calculation

Originally Posted by blueman
Reading page 21 and not understanding any kind of formula to determine this.

It says "determine what % of the SD the corresponding expected return represents" then find the area under the curve to the left of this figure.

Can you explain this in a pure mathematical formula? Like, how do i even make a curve?

I have EV of game and SD, isnt this all i need in order to find % win after x hands?
blueman,

Let's pick some numbers to see how to calculate your answer. Let's assume you're wonging in with a 2% edge (so at about +5) and flat-betting (so your S.D. is 1.15). If you play 100 rounds, what is the chance you'll be even or ahead?

Well, in 100 rounds, you expect to win 2 units. The total S.D. will be 1.15*?100 = 11.5 units.

If you end up even, your z-score is z = (0-2)/11.5 = -0.17. In general, z = (result - mean)/(standard deviation).

If you consult Table 8.9 on page 147 of BJA3 (or else use the Cumulative Distribution function in, say, Excel), you'll see that the CDF for -0.17 is 0.4325: this means you have a 43.25% chance of being behind. Therefore, you have a 56.75% chance of being even or ahead.

Hope this helps!

Dog Hand

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Doghand, what is 1.15*?100 supposed to represent? Or maybe formatting is wonky?

Wouldn’t the SD be:

Var = 1.15^2 = 1.3225

Var = 1.3225 * 100 = 132.25

SD = 132.25^0.5 = 11.5 (units)

?

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Plot the derived Gaussian curve on graph paper. Then with scissors cut out curve and weigh on an analytical balance to 0.1mg to determine AUC (area under curve).

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