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Okay I've got a math question I was thinking about recently but am not smart enough to figure out my self (plz don't make fun if it's really easy).
Let's say I play blackjack and I am 49% to win every hand. If I played blackjack every weekend for 2 hours for the rest of my life, what would my chances at being a winner at the end be (if you need the figures, which you probably don't, let's assume I average 50 hands per hour and play 4000 hours in my life)?
I guess the answer is 49% but that doesn't seem right.
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Hey, I'm feeling a bit mathy, so I'll go ahead and answer the question.
To make the math easier (without really skewing the results much), let's say you either win $1 or lose $1 in each hand. There's a 49% chance you win a buck and a 51% chance you lose a buck. This gives us a nice
binomial distribution which is very easy to manipulate and evaluate.
Over your lifetime you'll play 4000x50 = 200,000 hands of blackjack. In the average 100 hands you'll win $49 and lose $51, so your expectation is -$0.02 per hand, for a lifetime expectation of -$4,000. Now the variance of your lifetime total is going to be about 2*n*p*(1-p), or 2*(200,000)*(0.49)*(0.51) = 99,960. To find the standard deviation we take the square root of this number, giving us a standard deviation of about $316.16. To have a lifetime win, you'd therefore have to beat your expectation by 4000/316.16 = 12.65 standard deviations. Since there is a roughly
99.99999999974% chance of being within 7 standard deviations, the odds of you being a lifetime winner at blackjack are going to be markedly worse than that. I'd say the odds that you win at blackjack over your lifetime are slightly worse than the odds that you get hit by two meteors at the same time.