Calculating Probability of A Win or Loss

I have a question related to calculating the probability of gambling results being the result of luck vs skill in games with uncertain edges. This comes up a lot in stuff like poker. Maybe an example will help clarify what I'm trying to figure out:

Let's say you are playing a game with standard deviation of 14, you're betting $1 at a time, and you want to know what the chances are of having a positive expectation after X hands (say, 500) given that you are up $250, or the converse, down $250. Is this possible? Thanks!

I don't see enough information to answer the question.

Quote: Dieter

I don't see enough information to answer the question.

LOL. I disagree. With an uncertain edge, the standard deviation is fabricated. And if he always flat bets, we can assume his bankroll is infinite for practical purposes. So since there is a 100% chance he will be up $250 and down $250 after 500 hands, I'm going with NO SOLUTION.

Quote: Sonuvabish

LOL. I disagree. With an uncertain edge, the standard deviation is fabricated. And if he always flat bets, we can assume his bankroll is infinite for practical purposes. So since there is a 100% chance he will be up $250 and down $250 after 500 hands, I'm going with NO SOLUTION.

Well, I suppose if we're attacking it logically, the chances of the absolute value of (bankroll @ round 500) - (starting bankroll) being greater than $250 are calculable based on SD, but I don't interpret that to answer the intended question.

If you want to know what your chances of making $250 are, you need to know what your chances of winning per round are. I don't see that.

Quote: Dieter

Well, I suppose if we're attacking it logically, the chances of the absolute value of (bankroll @ round 500) - (starting bankroll) being greater than $250 are calculable based on SD, but I don't interpret that to answer the intended question.

If you want to know what your chances of making $250 are, you need to know what your chances of winning per round are. I don't see that.

Is it possible to compute the probability of losing your entire bankroll with only the standard deviation and the edge?

For example say the SD is 3.0 and your edge is 1%. You start with 500, bet 50, and play 100 rounds.

I'm wondering because it seems for different games, you could end up with identical SD and house edges but dramatically different payout structures.



Eg:
probability/ net
Game 1(made up game)- SD: 2.91, edge: -3.0%
0.10/8.7
0.90/-1

Game 2 (modified 3 card poker)- SD: 2.84, edge: -3.02%
0.0022/40
0.0024/27
0.0326/6
0.0495/4
0.1694/1
0.7439/-1

Quote: bumblingfool

Is it possible to compute the probability of losing your entire bankroll with only the standard deviation and the edge?

Yes, in addition to the information you provided regarding bet size and rounds.

Quote: bumblingfool

Eg:
probability/ net
Game 1(made up game)- SD: 2.91, edge: -3.0%
0.10/8.7
0.90/-1

Game 2 (modified 3 card poker)- SD: 2.84, edge: -3.02%
0.0022/40
0.0024/27
0.0326/6
0.0495/4
0.1694/1
0.7439/-1

What? Best advice I can give...don't make up stuff.

Quote: Sonuvabish

Yes, in addition to the information you provided regarding bet size and rounds.





What? Best advice I can give...don't make up stuff.

How would I go about getting that? Is it a simple formula?

Well, I was just trying to given an example of games that that are very different but with similar SD and Edges (those numbers are correct based on the made up payout chart).