Quote:
Originally Posted by Robb
In general, 7 random starting hands (or 14 cards) would only have between 4 - 5 face cards. All we're saying is that there were fewer than normal, so maybe only 2 - 3. Just taking 2 fewer than normal still makes the premium hands more than 50% more likely than normal.
TLR was more right than I suspected. My error was in assuming only 2-3 A/F would be gone. TLR was right when he said about 3.8 (actually 3.66) A/F should be gone. His was TINY error. Mine was HUGE. So I recalculated all the odds for the premium hands. Here's calculations for both 4 and 3 A/F left. The true average should be approximately in the middle.
Given 3 A/F were present in the first 7 starting hands, and that the remaining A/F are 4A's and 3 of every other card, we would have:
AA (6 ways)
KK - JJ (3 ways each)
AJ or better (12 ways each)
KQ, KJ (9 ways each)
This is 69 out of 630 possible combinations, or 10.95%. In general, the probabilities of getting this range of hands is 104 out of 1326 possible combinations, or 7.84%
Given 4 A/F were present in the first 7 starting hands with the remaining A/F distribution being 3 of each, would have about a 9.05% chance of getting a premium hand.
RECAP OF REVISION:
TLR was right. On average, we expect 3.66 A/F in the first 14 cards dealt. The probability of being dealt AA - JJ, AK, AQ, AJ, KQ, or KJ is:
General Case (all 52 cards present): 7.84%
If 4 A/F present in first 14 cards dealt: 9.05%
If 3 A/F present in first 14 cards dealt: 10.95%
If 2 A/F present in first 14 cards dealt: 13.02% *
*This is corrected from earlier post. Yes, another mistake.
Wow. I really f***ed up. Sorry for the errors. It appears the true average for premium hands under these conditions are slightly less than 10% compared to just less than 8% on average. So, yeah, the blinds are going to have premium holdings 5 times out of 50 instead of 4 times. That's not really enough to make much difference in how we play. Good work, TLR!