Re: Dominated Outs
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Thank you, Aaron. I'm still using the "rule of 2" to estimate my chances of winning. That looks like a much more accurate way of counting odds. I think I'm going to start practicing permutation counts.
Someone else told me that Ed Miller calls these "discounted" or "partial" outs.
I agree that the trips are not as strong as the straight. I actually played the hand where the straight draw hit trip sevens. The villain bet 1/3 pot on the flop and checked the turn. In this particular case, I wasn't worked about a set. I was planning to let the hand go to any substantial raise, but he let me blunder into the win.
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The mathematical errors in using the rules of 4 and 2 are too minor to sit there and try to use combinatorics to come up with precise answers. Pot odds are not a bright line where its absolutely wrong to call on the bad side and absolutely right to call on the good side. There are enough other factors going on that make those minor "-EV" calls profitable and minor +EV calls unprofitable.
If you count runner runner draws as 1/2 an out when you have fairly few full outs, and as 1/4 out when you have a lot of full outs, you arent going to be far off.
A far bigger error is not discounting your full outs for opponents possible holdings, and not counting the opponents redraws. Eg if its a multi player pot, youve got AK and a dry flop, and its bet into you. Counting your AK as 6 outs to beat a probable pair may well be too generous. The chances of your A or K not being duplicated in another hand go way down and ignoring that possibiity is far worse than the errors arising from estimates istead of combinatorics
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