Recently i was playing Pick'EM (PE) and was trying to figure out whether more quads came from dealt trips or pairs. Dealt trips are much less common than pairs, but turn into quads 1/23.5 times, versus a much lower percentage for pairs. Based on experience, I would have said slightly more quads come from trips, but based on the following logic more should come from pairs:
In PE you are dealt 4 cards whci I will call A,B,C&D from l to r. A & B
become part of your final hand and you pick C or D which have 2 unseen cards under them to fill out your final hand. Of the 5 cards in the final hand in positions 1-5 from l to r, 1=A, 2=B, 3=C or D and 4 & 5= the 2 unseen cards under C or D. For quads from trips, 1,2,&3 are part of the quads and either 4 or 5. Thus the unmatched card must be in positions 4 or 5. For quads from a pair, 4&5 must be part of the quads, with the unmatched card in positions 1, 2 or 3; a 60-40 ratio compared to quads from trips. I realize there a certain pairs you will discard, such a high pair versus 3 to a RF w/o the A (relatively rare).
You also keep 3 to a SF over a low pair except a D.I. SF with no high.
These cases are not that common, and my questimate is that the ration would be decreased to more that 56-40.
Is there anything wrong with my "logic"? Thanks.
David
