.25/.50 pot limit like the title says, all the money goes in be4 any draws (very loose game).

im in position on villain. he draws 2 then 2 then....2 (YESS!!!).

hero has 2 3 5 8 Queen.

i would have had a hard time respecting myself if i patted this hand and lost. but what does the math say is the correct decision vs an opponent drawing 2?

pat.

2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: 2 2 3 3 7 7

Hand 0: 2 3 7 -- --: EV 45.7% - WIN/LOSE/TIE %: 45.7/54.3/0.0
Hand 1: 2 3 5 8 Q: EV 54.3% - WIN/LOSE/TIE %: 54.3/45.7/0.0

Dream scenario for villain still has you as 54% favourite.

thats so sick. thanks for doing that.

Yes patting we are a slight favourite, but we obv have a great draw if we were to break, and are still a favourite there. I would pat, but what are the equities of 2358 vs 247? Must be close between 2358 and 2358Q against it.

pokenum -l27 2c 3s 7d - 2s 3c 5h 8s / 2d 2h 3h 3d 7s 7c qh
5-card Draw 2-7 Lowball: 25308 enumerated outcomes
cards win %win lose %lose tie %tie EV
3s 2c 7d 10581 41.81 14718 58.16 9 0.04 0.418
8s 2s 3c 5h 14718 58.16 10581 41.81 9 0.04 0.58

This format is pretty hard to make out, but I'm assuming that 58.16% is the important number. So I'm guessing that this means that we would have 58% rather than just 54% if we were to break?
What exactly are those numbers on the first line? Is it including (guessed at) dead cards?

Hand text is hard to decipher, but if villain is drawing two on the last draw, we are a favorite and should pat. We'll still be a favorite if we draw, but the implied position doesn't argue for trying to improve since we can only make an Eight and will induce some bluffs staying pat.

What? This doesn't make sense. And we are all in already, so there is no betting street after. But anyway I wouldn't think that the possible bluff- inducing would be a positive, people are almost never going to be bluffing in that spot from drawing two.

Sorry, I forgot we were all-in.

If not, we're not drawing to a hand that can suffer multiple bets on the river and like it. We need to make an Eight perfect to feel good about raise/call.

I don't like drawing when I know I'm breaking a solid favorite, but I can accept that there is an emotional component to that preference. I don't like knowing I risked degrading a hand when improving wouldn't earn much. In OP's case there isn't an implied position to take advantage of so the benefit of improving is muted.

Tbh I don't think that any of this really matters. Imo it all comes down to which of the two options we are more of a favourite with. If (according to the above results) we are a 58% favourite if we break, rather than a 54% favourite if we keep the Q, then I'm breaking.

And I just put it into the calculator as well. Not sure what I did differently, but I got pretty different odds to above, making us a significantly bigger favourite.

With no dead cards:
2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: none

Hand 0: 2 3 5 8 Q: EV 68.5% - WIN/LOSE/TIE %: 68.5/31.5/0.0
Hand 1: 2 4 7 -- --: EV 31.5% - WIN/LOSE/TIE %: 31.5/68.5/0.0

2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: none

Hand 0: 2 3 5 8 --: EV 64.4% - WIN/LOSE/TIE %: 64.4/35.6/0.0
Hand 1: 2 4 7 -- --: EV 35.6% - WIN/LOSE/TIE %: 35.6/64.4/0.0


With some arbitrary dead cards:

2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: 2 2 K J 8 5 J A

Hand 0: 2 3 5 8 Q: EV 66.2% - WIN/LOSE/TIE %: 66.2/33.8/0.0
Hand 1: 2 4 7 -- --: EV 33.8% - WIN/LOSE/TIE %: 33.8/66.2/0.0

2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: 2 2 K J 8 5 J A

Hand 0: 2 3 5 8 --: EV 68.2% - WIN/LOSE/TIE %: 68.2/31.8/0.0
Hand 1: 2 4 7 -- --: EV 31.8% - WIN/LOSE/TIE %: 31.8/68.2/0.0

The arbitrary dead cards sim is meaningless. We have no dead card information.

We've seen at least two cards we don't want, and villain has discarded six cards he doesn't want.

We don't know which cards. Which cards matter, so we should not make any assumptions about them.

So Cockboat and TheGusPair, (other than different dead cards) what did I do in my calculations that made my equities so different from yours?

Disagree. Some assumptions at least can be made. E.g. which nut cards matter, and which pairs are obviously being discarded. And those kind of assumptions do affect the equities a little, but not much, e.g. an Ace dead card is not very different from a paired 2. The only time it would really affect the equities would be if one of the dead cards was a pair for one of the players, but one of the nut cards for the other (which is why I erred on the side of choosing dead cards that were obviously very high cards, and pairs for both players.
And I think overall it gives us a better idea of the true equities than if no dead cards were used.

We know that villain would always discard an Ace, and that he would discard e.g. a 6 less than 50% of the time.

The only difference is the dead cards, which is why making educated guesses about them is a good idea.

I disagree that we can know which cards villain has, which ones he paired, how smart he is at drawing, or basically anything else about what cards are dead. We don't even know which cards Hero discarded. Unknown cards are unknown.

Do you disagree with this? If not, do you agree that this makes the deck (slightly) skewed towards low cards?

Hero Value shows the sort of effect this has, it would be interesting if someone more skilled at combinatorics than I am could do some more precise simulations.

Doing a tree for all of villain's possible hands, plus all of hero's possible discards would allow you to weigh the probability that any particular card was discarded as a pair, but we don't know for example if villain would discard a Ten on the second draw, draw two if he held 3456 etc. We have no idea. Unknown cards are unknown.

That is an example of two close decisions, which are quite specific and not so common in the scheme of all the cards/situation. Drawing to possible straight cards is also not applicable in this case as villain has a completely clean draw. The - pair for one person, nut card for the other person situation I think is a lot more significant.
And because the "would they keep a 10" -type spots are generally close, and relatively rare in terms of all the cards in a spot like this one, I don't think that they should factor a great deal into our calculations. And no offence, but Just continually saying that "unknown cards are unknown" sounds almost kind of naive/ignorant. Making educated guesses I really think give us a better idea, and (as shown) bring us closer to the true answer.

Agreed.

against an aggressive opponent who often 3-bet/draws 2, what type of hands would you 4-bet, assuming after 4 betting that a high % of the time all the money will go in be4 any draws (opponent is a gambler)?

What did you discard in the hand you posted?

I just think it's a bad idea to intentionally skew a sim based on presumptions we cannot make with any accuracy. If villain paired a card we need and discards it, that's way worse for our draw than if he discards a King, for example, and it would be just as possible to construct plausible dead card scenarios that make our draw lose a lot of its equity.

I agree that there is potential for a large analysis matrix that assigns probabilities to certain dead cards, but just picking some out and sticking them in the sim is going to be deceptive and less helpful than accepting that you don't know what the dead cards are.

Unless I'm 4-betting to isolate a pure fish who is dusting off his money, I'll rarely 4-bet PL without a strong pat hand or near perfect draw.

In limit games you should 4-bet villains of this type with good three-card starting hands including paired discards or any four-card draw to a good 8 or better. Weaker pat hands should be 4-bet if you're certain this will allow you to get HU with the loose opponent, folding bad pat hands otherwise. Breakable weak pats you can 4-bet regardless because you can break if OOP in a mulitway pot and maintain a drawing advantage.