how to calculate equity that isnt 50/50?

[b33nz]

ive been wondering what formula do i use to calculate equity that doesnt happen equally.

what i mean by '50/50' is lets say you are gonna win $100 50% and lose $50 50%. so then its easy you just take 100 - 50 = +$50 on average.

but now lets say you are gonna win $100 75% and lose $50 25%. what formula would i need to calculate the correct amount?

[Boredom]

Actually I think in the first example you gave, $25 is the correct answer. Consider you do two trials, first one you win 100, second one lose 50. You have won 50 bucks, or 25 per trial. Over a long sample you would expect your results to be nearest this hypothetical result (half wins and half losses) so the expectation should remain close to 25 bucks per trial.

So what you need to do is do the 100-50=50 and then divide by two to get the expectation per trial.

In the 75% win 100, 25% lose 50 it's easy because of the round number percentages. (100 + 100 + 100 - 50)/4 gives an average expectation of 62.5 per trial.

What I'm unclear on is how to do it when the numbers aren't so neat, for example 76% win 100 24% lose 50 or something.

[Boredom]

One way of doing 76% win 100/24% lose 50 is to multiply 76 by 100 (7600), then subtract 24 times 50 (1200) (this difference giving us the average expected result per 100 trials), then divide this number by 100 (for average expected result per trial). The answer is 64, which looks right assuming I got the 75%/25% work right in the previous post.

[Boredom]

Basically if you can figure out the average result of a manageable number of trials, you're halfway there. In a coinflip (ie 50% x, 50% y) scenario, it's easy to determine the average result of 2 trials. One of x, one of y.

The more trials you do the closer your overall result will abide by this pattern.

Then there is simply to divide this average result of (in this case two) trials by (in this case two) to arrive at the average result of one trial.

So in a 75% scenario, we can easily find out what 4 trials will result in. Since 75%-25% is the same as 3-1, we take 3 of the 75%-likely scenario (in this case +100x3) and 1 of the 25%-likely scenario (-50x1), add these together (300-50) and divide by 4 for average result (since we have been studying the average result of what four trials would be).

The reason I was so longwinded in my response is that I don't think about this stuff enough myself, so thank you for the opportunity. [img]/images/graemlins/grin.gif[/img]

[b33nz]

you were right about my original example. but i figured out how to calculate it easily even with not so neat numbers.

examples:

win $100 50%, lose $50 50%:
( 100 * .5 ) - ( 50 * .5 ) = 25

win $100 76%, lose $50 24%:
( 100 * .76) - ( 50 * .24 ) = 64

[Boredom]

Beautiful.

Nice teamwork, go us! :-)