How many trials to physically prove or disprove a certain edge really exists

Howdy to the Community, I have a probability/statistics question that I would like a little help with if possible. If I play any gambling game that has a "supposed" negative edge against the player of 1/2 % How many physical trials (hands) would it take to prove out or disprove that the 1/2% negative edge really does exist. I have heard that you can never be 100% certain but you can say something like, after X number of hands, I have 98% confidence that results of the trials will match the true edge of the game. the forums are great and thank you to the creators and admin folks as well as the members that make it super... Thanks, bklyn PS I look forward to the B&M places going to back to 6 spots.. post covid


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There is a statistic called N0 (N-zero). It gives you the number of trials (hands or rounds) you must play in order for your expectation to equal one standard deviation. At that point, using the normal distribution, you can say you have a probability of about 84% of being at or above expectation. At 4 x N0 trials, that probability increases to approximately 97.5% and at 9 x N0, it approaches 99.85%.

N0 is calculated as variance / (ev^2) or (standard deviation / ev) ^ 2 [where ^2 means squared]
HI Gronbog, Thanks a lot for the help. I am not exactly a math wiz, can we do the calculation right here on the forum, do we have enough info to even begin solving for the answer, all we have right now is the edge value. I don't know where/how to go from there. Thanks, bklyn


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Depending on exactly what the bet is, it may be possible to calculate standard deviation, but in those cases the ev is probably also able to be calculated and there is nothing to prove with respect to the reality of the edge.

For more complex cases, like blackjack (which I might infer is the case here based on your stated 0.5% disadvantage), we obtain the ev (edge) and standard deviation by simulating the game. However in that case, the simulator can also calculate N0 for you.

I'm just now noting that you are trying to demonstrate a 0.5% disadvantage. In that case, the probabilities I quoted above are those for being at or below expectation. Forgive me, we're mostly concerned with working with advantage situations here. ;)
Yes, Thanks so much for hanging in there with me. I need to be more clear. You are correct, the game is blackjack. Here is what I am trying to discover: 1. I know what the negative expectation should be. under normal circumstances 2. If I have a method that I think can "beat" (nullify and reverse)that negative expectation, I would need to do enough physical trials or computer based trials (hands) to demonstrate or prove out that using the method really does that. So the clear way of saying this is: I have played X number of hands of blackjack with this casino rule set and number of decks, with a bet of Z dollars per hand and by NOW I should be losing roughly Y dollars but I am NOT and the fact that I am not losing the expected amount of dollars gives me a _____________________%_ certainty that whatever I am doing is making the negative edge disappear, because by the time the X number of hands has been played, there was a ____________% certainty that the assumed or postulated edge would have shown itself as real losses somewhat close to the expectation of negative 1/2% against me. So again we are back to the question of how many hands trialed will allow me to make that conclusion at various levels of certainty or confidence. thanks, bklyn


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The answer is the same, but you're complicating things a bit. You're playing blackjack and you have some strategy that you believe will make you a winning player. But rather than try to calculate the probability that, when you're not losing, it's due to your strategy, you should just simulate using your strategy using software. If it's a card counting system, then CVCX or (if it's something complex, CVData) can do that for you. If it's something beyond counting, hole carding or other well known strategies, then there may be no existing software to help you.

The results of the simulation will tell you the advantage (or lack thereof) for using your strategy and other useful things, like how much you should be betting, risk of ruin, variance, N0, bankroll requirements etc. for what you are betting.

Blackjack strategies are too complex for simple calculations. You really need to simulate your strategy.

I see that you're new here, so let me say that, if it's some kind of progression or money management strategy, then forget about it. Those can not overcome the house edge.