Why does everyone think that these extremely tiny statistical examples are worthwhile? You don't need millions of
hands, you need millions of millions of hands.
Think about this - How many different ways can a deck of cards be arranged? Well, at the top of the deck, there can be any one of the 52 cards. The second card down will be any one of the remaining 51 cards, so statistically speaking, there can be 2,652 different combinations of cards in just the top two cards in a deck. Adding the 3rd card multiplies 2,652 by the 50 remaining cards for a total of 132,600 different combinations for the top 3 cards. To compute the total number of different combinations for an entire deck of cards, we would have to multiply 52 x 51 x 50 x 49 x . . . . x 3 x 2 x 1. The mathematical term for this if 52 factorial or 52!, which is multiplying 52 times every number below it.
So, if we continue on down through the numbers. . .
At 10 Cards - 57,407,703,889,536,000 combinations
At 20 Cards - 306,532,583,223,110,000,000,000,000,000,000 combinations
At 26 Cards (1/2 Deck) - 2 x 10^41 or 199,999,709,752,404,000,000,000,000,000,000,000,000,000 combinations
Full Deck - 8 x 10^67, or 80,658,175,170,943,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
So when you look at how 1,000,000 hands are dealt, you will see statistics start getting closer to the norm (1 out of every 221 hands or so) - but still don't be surprised if it's one out of every 230 or 210.
The whole concept of a
poker site (or a real casino) rigging anything is just outlandish to me. They will make money hand over fist following the rules and not rigging anything. The next thing that we're going to hear is that the
poker sites have two different rules - one for the low limit tables and one for the high limit tables - the high limit tables aren't rigged (if they were, why would the poker pros go there), but the low limits are.
Ironically, as I was posting this thread, I was playing the CardsChat Saturday freeroll and was dealt my second set of pocket As today. I ended up losing to a pair of 4s that hit trips on the turn and quads on the river. I suppose this is where I could blow up and scream about AA being rigged, but I think I'll go the opposite direction -
IT'S POKER - SH*T HAPPENS!