Math and a Lifetime

[Talking Poker]

Gov - your concept of the "long run" is off. While a TRUE long run may be millions and millions of hands/flips/whatever, the numbers will statistically work themselves out much, much faster than you are suggesting.

For example, with your million coinflip, no way will the numbers be 520k - 480k. That's 20k/1MM = 2% variance and it just won't be that high after 1 million flips. I forget all the fancy terms (Standard Deviation - ooohhhh) and formulas from my stats classes back in the day, but I'mn telling you, it won't be this far off.

And same goes for your AA vs underpair scenarios. After 10k tries, NO WAY will the AA only win 30% of them. It's impossible.

If you want to prove it, and since you have the time, start dealing! Deal out AA and pick a random underpair. Then shuffle the rest of the deck and deal it out. Then reshuffle and deal it out (no need to reshuffle the two pairs). Rinse and repeat and record your results. Do this 1 million times or so, and I'll guarantee that at no point in the million hands was there a stretch of 10,000 where the AA only won 3000 times.

You could of course use a computer program to do this much faster for you, but like you said, you've got a lot of time on your hands.