[Paul2432]

First of all some of you math is off. The correct way to calculate the probability of a card appearing on the flop is to calculate the probability of it not appearing, and then subtracting that value from one. In the case of flopping a set we get P=1-(48/50)(47/49)(46/48)=11.755%. Likewise for flopping and ace P=1-(46/50)(457/49)(44/48)=22.55%. These numbers are pretty close to yours anyway so I agree there is some explaining to do.

Whenever, an event either happens or doesn’t happen, you can use the binomial distribution function to determine the probability of a particular number of results in a particular number of trials. If you have Microsoft Excel, this can be done quite easily. (note that you want to use the cumulative binomial distribution function which calculates the probability of a particular number of trials or less, not exactly that number of trials).

That said, I get these results:

After 1675 pairs seeing a flop, the probability of flopping 168 or fewer sets is 1.4%

After 93 pocket KK seeing a flop, the probability of seeing 29 or more flops with an ace is 3.4%.

These results might seem suspicious but you need to keep a few things in mind. First some perspective. The probability of rolling a 12 while playing craps is 2.8%. You have seen results around as likely as rolling a 12. Second, developing a hypothesis (that Party’s deal is not fair) after looking at the data does not constitute proof. Hundreds of statistical anomalies are possible in the data. For example, you could flop flush draws when holding a suited hand or straight draws with a connecting hand at improper frequencies. That a couple of statistical anomalies are found is expected.

If you truly believe the flops are not fair develop your hypothesis and then collect the data. Keep track of your next 93 flops with KK and your next 1675 flops with pocket pairs. If these results repeat then you might be on to something.

Paul