Quote:
Originally Posted by river.king
- The odds of hitting the exact same flop within 10 flops are 17,582,760,000/10 or one in 1,758,276,000 times.
Assuming you care about the order of the flop, I calculated that it was 1 in 2947.
Chance of a duplicate flop appearing in 10 hands is the same as:
1 - (Chance all 10 flops are different)
= 1 - [(132599*132598*132597*.....132591)/132600^9]
= 1 - (0.99966068)
= 1 in 2947
You were off by a factor of just over half a million....
Your set of 6000 hands has 5991 sets of 10 hands (Hands 1-10, Hands 2-11, Hands 3-12.... ) but these aren't independent. We can take a gigantic underestimate and say that there are 600 sets of 10 independent hands. (Hands 1-10, Hands 11-20,...). Note that this is a big underestimate because, for example, you could have witnessed the same board on Hands 368 and 372 which are only four hands apart, but are treated as being in different groups of ten by this method.
Then the chances you don't observe an identical board within some set of 10 hands is 2946/2947^600 = 81.5%, or the chances that you did observe it are 18.5%. Note again that this is a *gigantic* underestimate. It wouldn't surprise me if the actual result was well over 30%
If you don't care about the order the cards are dealt, i.e. QJTddd is the same flop as TQJddd etc... then it almost impossible that you would *not* have seen the same flop within the space of 10 hands at some point in a 6k hand sample.