Quote:
Originally Posted by NoLimitNinjaBri
There are 8 x 10^68 ways to shuffle a deck of cards. Multiply that by the number of seats at the table, and I think that represents the total "long run".
Can someone who is more learned on the subject tell me what a statistically significant sample would be based on that population?
You're mixing up two things here a bit. The number of combinations of cards and seats isn't particularly relevant, because
a) the effective number of combinations is way lower because from your point of view, many combinations are functionally equivalent. For example in a 10 player game, there are only 25 cards in play, not 52. Then there are situations that are functionally the same such as Kh5s vs Kc5d etc.
b) the actual number of combinations doesn't really matter as much as the distribution of outcomes. For example. Say we're going to play a game where I write down a number and without looking at it, you guess whether it's odd or even. The sample space is infinite - but the "long run" is very short because you have a 50% chance of guessing. It's quite easy to calculate how often you'll guess 5 times wrong in a row, or how often you'll get 10 wrong in a row out of 1000 guesses, etc.
The worst case for variance is actually 50/50. There is a formula for estimating how many iterations you need before you have, say, a 95% chance of being within 1% of the "true" outcome. I have it here:
http://rustybrooks.com/poker/monte_c...imulation.html
it's a lot smaller than you think.