Re: Full house odds in O8 (cross posted from Probability)
I'll try. No promises as to correctness.
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What's the probability that a set on the flop will make either a boat or quads in 08?
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Assuming you don't already hold any of the potential board pair cards, you have 7 outs.
full house (read or better) on turn: 7/45=15.6%
full house on river given none on turn 10/44=22.7%
turn or river: 0.156+(1-0.156)*0.227 = 34.8%
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For bonus points, if there are two low cards out when you flop top set, what are the chances that no low will be possible if you fill up.
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Assuming you hold 4 high cards...
given full house on turn, low appears on river 24/44=54.4%
given full house on river, low appears on turn 24/45=53.3%
1-[(0.156*0.545+0.533*0.227)/(0.156+0.227)]=46.2%
Slim
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