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
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
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)
?
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
Bookmarks