Hi,

HJ is 23/20 @ 130 hands
CO is 88/0 @ 17 hands

Given villains stats I'm limping in on the btn. With an OESD considering 2 cards to come I'm good 32% of the time (8*2*2) and pot odds tell me I need to be good at least 25% of the time so I call. On the turn considering river to come I'm good 16% of the time and pot odds suggest ~42% so I fold.

Is that correct? I am a bit confused with all that counting but I think I might finally got it. Some people say in general that if villain is betting more than half the pot you should lay down any draws, but I think that might be over-generalization.

And sorry for asking such dummy questions here.


PS. I know that number of outs * 2 is a shortcut, but I am trying to teach myself to count those things in the head while playing.

The way you played the hand is fine but your reasoning is wrong in many ways.

Chance of making your hand by the river with 47 unknown cards depends on how many of the 1081 possible runouts lead to you winning *. Now that's hard to calculate in game so as you say, we use the shortcut with outs. Like in your workings, adding one out makes about 2% of the turns, and 2% of the rivers swing in our favour, so we can count 4% per out. Beyond a certain point though, when we add an extra out, some of the runouts it is in would already have been ours anyway - if a runout has two of our outs we don't win double the pot - consider, JT vs 22 on 988 - we have 24 outs but we don't have 96 percent equity - we still lose 30% of the time when we miss twice in a row. For more practical numbers of outs it's good to use the rule of 4 up to 8 outs/32%, then count each additional out as only 3%, so 9>35%, 10>38% etc.

The above is a good rule of thumb but it ignores the effect of redraws - JT on 367 wins 37.44% against AA but only 25.56% against 33 - there is one fewer out (the 9), but the main reason for the difference is that even when the flush hits, villain has 10 outs on the other card of the runout to make his full house/quads

There can also be runner-runner outs, in the above example if you change the 7 to 9 the runner-runner straight draw comes in about 2% of the time (another reason why JT is weaker against 33 is the removal of the runner-runner 2-pair outs).

Next point, all the above is our chances of hitting the straight by the river, but you need to pay 25% just to see one more card, you aren't guaranteed to see the river because he might bet you off on the turn (as actually happened). To work out your chances of hitting on the next card, use the rule of 2 instead (8*2% = 16%). So your immediate pot odds are not good enough. However it is possible to call much wider than immediate pot odds allow - some of the time you might be good anyway (e.g. last night playing live I won with a Jack high missed straight draw after calling what I assume was a semi-bluff from a lower straight draw) - real hands are very often a mix of draw equity and showdown equity - that's unlikely in this hand with two people putting in money in ahead of you but you should remember it if you have overs to the board - they may also be overs to someone else's draw. The main reason though is implied odds, if your A, and particularly your 9 hits on the turn, you don't just win the money in the pot at that point, you win all the money that goes in on later streets - they aren't just going to shut down because the turn is 9, they'll likely keep firing and you can check-raise.
On the turn, again you have 16% - though someone can back-door a flush on you - and there is also one fewer street to get money in. If the river is the 9 you are still probably good but it's harder to get money in. AK may just check behind, so I like a fold here - you only have good implied odds on one street with 6 of your outs, the other 2 might lead to you putting in money with the worst hand (though it makes a big difference that MP can't have both a K and the flush draw) but most likely they kill your action, whereas before you had potentially 2 streets of implied odds with 8 outs.

* Actually for a given opponent holding that we are supposed to be able to beat, it's 990 possible runouts of the other 45 cards. For this hand it's worth mentioning that they definitely have A blockers to our draw in their ranges so you might be on 7/45 outs when they are turned over rather than 8/47.