Quote:
Originally Posted by PokerPlayingGamble
So, we could go for a hail mary, and play the king up top and the seven in the middle. Then we have a roughly 6.25% chance of rivering the 9 in the bottom (plus every once in a thousand times we will make a tight nines full of jacks). We win a lot when this happens, but even if the gain from making strong hands + fantasy land is in total 30 points when it does happen this is only worth just under two points because it happens so infrequently.
Next we could play to not bust, by not making kings on top or three of a kind in the middle. There are a few ways to do that.
We could also play something like K up top and queen to the bottom. The middle is still live, with two fours and two threes to hit. RHO opponent had 32 in the middle so it is unlikely he discarded a three, although LHO had no reason to keep either a three or a four. Hitting both a four outer in the middle and a two outer in the bottom is also very unlikely, even with only a pool of 16 cards to draw from.
I guess Q up top and king on the bottom is the way to go. Strong chance to prevent the scoop with AKQ (there are very few live broadway cards) and we can still draw to beat RHO on middle and bottom.
I think your bolded math is wrong. I assume you don't have a 9 in your discards. If so, we have seen 36 cards, so there are 16 remaining. We get 3 of them. Chances that none of those 3 is a 9 is 15/16*14/15*13/14=81.25%. So we have about a 19% chance of hitting the case 9. I'm not able to calculate your chances of going runner/runner if you put the K up top and Q on bottom, so hard for me to evaluate that option. However, with Qs dead and only one live J, doing so gives us one extra out on the bottom while requiring us to hit in the middle too, so doubt it is better than 19%, and also gives up the royalties and winning in the middle plus the (admittedly unlikely) possibility of hitting a boat on the bottom. So I'm going to assume our choices are playing Q up top and 7 in the middle v. playing safe just to set.
I think I go for it (though hard to say without knowing your discards). We really aren't doing very well if we play just to set. LHO has 2 live aces. If we don't make any assumptions about the other people's discards, he's about 35% to hit his ace and scoop you even if you play safe. If you assume no one has discarded an ace, then he has 2 aces with 10 cards left, and his chances of whiffing on the aces are 8/10*7/9*6/8, or 46.7%, and he's actually a 53.3% favorite to bink his ace and scoop. Truth is probably somewhere in the middle but he's probably at least 40% to scoop you if you play it safe. Similarly, RHO has 2 outs to scoop if you play it safe, a K and a J, so his odds of scooping you are similar (though probably a little worse as it's more likely someone has mucked a J than an A). So even if you play it safe you're usually getting scooped by at least one of your opponents, and sometimes by both of them. You're not putting any royalties at risk by going for it. If you bink, you definitely don't get scooped by either of them, and are reasonably likely to scoop v. RHO.
Without running through all the math, I think I'd play this aggressively and put K up top and 7 in the middle. If this were progressive (such that you get 15 cards in FL for KK up top) I definitely would.