Making sense of statistics
Sometimes it's just too difficult to translate statistics into an actual model or simulation so let me just ask. If I used solid basic strategy in blackjack, and played 1000 hands, statistically I should have won 475 hands and lost 525 hands. Correct? My question is what would be the breakdown of the 525 losing hands? How many single losses, two in row, three in row, etc.? It seems to me that it would be 262 singles, 131 @ two in row, 65 @ three in a row, 33 @ four in row, 16 @ five in a row...and so on until it addes up to 525. Is this Correct? To just divide in half down the line? That doesn't seem to jive with the wizards math of using .5251 x the ? power.
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If you post this as a question in the forums you might have more chance at an answer.
262 singles, 131 @ two in row, 65 @ three in a row, 33 @ four in row, 16 @ five in a row..
That would add up to 262*1 + 131*2 +65*3 + 33*4 + 16*5 =931 losses.
Out of 1000 hands you would have a
76.523% chance of at least one streak of 9 or more losses in a row
93.862% chance of at least one streak of 8 or more losses in a row
99.554% chance of at least one streak of 7 or more losses in a row
99.998% chance of at least one streak of 6 or more losses in a row
and very close to 100% of shorter streaks.
That is not exactly the answer to your question, but it may help you. There is an algorithm to do this calculation, but there is no algebraic formula. I'm not holding out on you.