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Message: [QUOTE="zachvac, post: 725766, member: 26306"] Here's the thing, you're dealing with an ex post facto calculation. I'll do it in a sec but let me explain the dangers of this. There are so many ways in which you can be unlucky in poker. You can miss sets more than usual, you can get dealt AA less than usual, your AA can hold up less than usual, etc. When you pick one thing to examine it's usually the one that's the furthest from the mean statistically meaning that you are selecting a small portion of the data because it is abnormal and treating it as if it is all the data. And example would be you flip a coin 100 times. There are 5 heads in a row. You say "wow, the odds of 5 heads in a row coming are 0.5^5 = 3.1%. Never mind that it's very likely for that to happen in the entire sample, but you just picked the most out of the ordinary data and isolated it. If after flip #43 you say "let's see how many heads we get in the next 5 flips" and then they're all heads, that's something somewhat unlikely, but when there is much more data and you pick one stat to use, and the reason you pick the stat is because it's probably low, you're not using sound scientific or statistical reasoning. But say going in you had said you were going to examine the number of AA vs. expected. Using a 1-proportion Z test (google it, we learned how to do the calculation in HS stat and I could look it up but my calculator has a function for this so I'll let it do all the work), we get that getting your data or worse (further away from the mean, as in less AA's) is 1.65%, pretty unlikely (just for reference the political polls use 95% confidence interval, so anything below 2.5% is outside their range including the + or -. Yes you've been unlucky with AA. It's not unbelievably unlucky but you are in the bottom 2 percentiles of the poker population in terms of how often you get AA. Also along with the ex post facto comment is selection of people in poker as well. If something is 0.001% = 0.00001 to happen, we would usually dismiss it as close enough to impossible. However, when we have hundreds of thousands of people playing poker, and they are playing thousands and thousands of hands, all of a sudden the odds of one person having that happen to them is actually pretty likely. Sort of like the lottery. Bad enough odds that I can say that statistically it's pretty much impossible for me to win, but some people win, right? When you have that many people who play, the odds of ONE of them goes up. Your personal odds still stay the same, and each individual person can more or less say that they won't ever win the lottery, but one of them will be shocked and will be one of the luckiest people in the world and hit their number. By the way, runner runner to 2 outs (as in they have to hit exactly 2 cards in the last 2 to win) is 1 in 1081. The odds of winning the lottery are 1 in 80,089,128 for the powerball ([url]http://members.cox.net/mathmistakes/rawdata.htm)[/url]. Catching back to back runner runner draws (to exactly 2 cards, example is opponent has nut flush and you have a straight flush draw on the turn to exactly 2 cards. example opponent has AJs you have 34s flop comes 789 all the same suit as both your hands. The odds of winning this back to back is:) 1 in 1081^2 = 1 in 1,168,561. So you are 80 times worse to win the lottery than you are to win back to back runner runner to exactly 2 cards draws. If this person got this kind of luck in poker on an opponent, they would certainly cry how poker is rigged, how they're nut flush got runner runner'd to a straight flush twice from the same guy and then the very next hand rivered a 1-outter on him (that's about the 1 in 80, lottery is still less likely than this because 1-outter is better than 1 in 80). But when someone wins the lottery it's always "well someone has to win it". So next time you take a horrible beat, think of it that way. The odds are such that it will happen, and someone has to take that beat. Unfortunately it was you, but that's the way it goes. [/QUOTE]

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