Dominated Outs

[Alan3]

I write a poker blog in the hopes that people will let me know when I am wrong, but I rarely get that there. I had a flash of insight this morning and wrote an entry. I'm hoping that someone here will be able to tell me if I'm wrong --or just being stupidly obvious. In any event, I hope someone gets something out of it.

In math, when one part of an equation contributes more to a curve than another part we say that the bigger component dominates the second component. This happens a lot in the analysis of algorithms. Say we analyze an algorithm and determine that it takes n^2+n operations to run where n is the size of the data. As n grows large the n component of the equation becomes insignificant compared to the n^2 component and it is often just ignored.

When you are trying to figure out if you have odds to call a bet or making sure you bet enough to get your implied odds on when you chase you are probably just counting the dominant outs. Consider this situation:

You have 76 on a flop of A85 rainbow. An opponent bets and you are sure he has an ace. You count eight outs to make the straight for around 1:5 odds against. Any bet you put in needs to pay off five times (including the amount in the pot) to make chasing this hand worth the risk.

Say you chase and instead of the straight you catch runner runner sevens. The odds against that happening are 1:359. The only way you would get the correct odds to chase that would be if everyone else at the table checks. But those longshot odds are still included in your real odds to chase that straight -- they are just so small that they are not worth counting. If you are on a straight draw and catch runner-runner to make trips you still only need to paid off 5:1 to come out ahead in the hand.

Next time you are on a flush draw with bottom pair and TPTK pays you off handsomely when you runner runner a boat, when he calls you a suck-out just say, "I had outs."

[Copernicus]

not wrong, obvious, and not enough to do with domination to make people read about it

[AaronBrown]

324 (8*7/2 + 8*37) of the 990 (45*44/2) boards give you a straight, 15 (6*5/2) of the remainder have both cards 6's or 7's and thereby win anyway. That's about 1/3 of an out.

However, these boards are not as good as the straight boards. In the first place, you have to wait for the river to know you've won, while over half the time that you get a straight, you get it on the turn. Also, with a straight you know you've won unless the board also pairs. If you get two pair or three of a kind, you could lose.

[Alan3]

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.

[Copernicus]

[ QUOTE ]
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.

[/ QUOTE ]

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