to play Qc3s5s

Hero :

Qd
Ac9c8h
JdTcTd2s2h




Villain :



AsTh
6c3c2c
Kd8d7d6d

IMO the best play is to play the queen on the top. You are taking a substantial risk in busting, because you can only be saved by getting either one of two aces on the final draw, or both an eight and a nine. IIRC you will get an ace about 20% of the time in this situation, so we have around a 25% chance of getting fantasy land imo, maybe slightly higher.

A few important points :

At the moment we have no royalties. So really we are only risking getting scooped, which is six points. By going for fantasyland we gain +7 for the queens, the value of fantasy land, as well as potentially scooping ourselves or almost certainly winning two/three. Villain is very likely to make his flush but will probably have to safety out with a pair on the middle. If we safety there is a strong chance we get scooped as well because we will have basically nothing anywhere.

LHO :

AsQd
5s5c5d4s
JhTc9h8s7s


RHO :

KhJc
6h6d3d2s2h
qsqh8h8c


hero :


AdKs
7c7d4c3h
Js9s9d


to play :


7hQcKd

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.

OK, decided to go into a bit more of the math. Based on my post above, I'm going to assume that if you play it safe, you get scooped by one but not both of them. You won't have any royalties, so that's probably worth -7 or so. The possibility that you don't get scooped by either is basically offset by the possibility that you get scooped by both. If you go for it and whiff you're at -12. If you bink, you get 10 in royalties v. each player (8 for KK up top, 2 for trips in the middle) for 20 points, you get to go to FL v. each player (say that's worth 8 points each) for 16 points, you almost always scoop RHO (6 points) and you maybe get +1 or -1 v. LHO (average of 0). So I have binking as worth 42 points. Note I ignored the possibility you hit a full house on the bottom, which gives you 12 more in royalties and means you usually scoop LHO for an extra 6 points. You're just south of 1 in 5 to bink, so your expected value is around 8. 4/5 of the time when you whiff your expected value is about -9. So all told I have going for it as giving your hand an expected value of around -1, while playing it safe is worth -7, and think you should go for it. Even if you increase the value of your hand for playing it safe considerably, you're not going to get it up to -1.

Looks to me like (i) you're underestimating your chance of hitting the case 9, (ii) overestimating the value of your hand if you play it safe because you're still pretty likely to get scooped by at least one of the other players and (iii) miscounting the value of hitting, which I have as a bit over 40, rather than 30.

Just doing the math again, you have 2 aces assuming none are in your discards. If we make no assumptions about the other guy's discards, we've seen 23 cards so there are 29 remaining. That means the chances of whiffing on the ace on your last draw are 27/29*26/28*25/27=80%, so you have a 20% of hitting an ace, plus some chance I can't quite figure out of hitting 8 and a 9. So let's put it at 25%, especially because it's usually a fair assumption that your opponent hasn't discarded any aces here.

If you bink, your hand is worth 7 royalties for QQ, 8 for value of FL, and probably +1 for winning 2 out of 3, so value is 16 or so. If you whiff, your hand is worth about -6 (a little less because sometimes our opponent fouls too). So that means if we go for it our hand is worth 1/4*16-3/4*6, which is around zero. If we play it safe, it's hard to gauge our hand value. Usually we get scooped and we're at -6. Every so often our opponent fouls and we're at +6. Sometimes our opponent sets and we win one or two lines and we're at zero. All told, we're much more likely to get scooped than to scoop here, so our hand if we play it safe is worth well less than zero, and again we should play it aggressively.

I think the lesson I take from all the math I've just done is that when you're not risking any royalties, and when your opponent/opponents look pretty unlikely to foul, it's usually a good bet to play aggressively for FL even if you're pretty likely to foul yourself with an aggressive set. You're just not risking that much and the rewards of FL are usually at least 16 points (7 of royalties, value of FL and winning the top line).

for the Q35 hand hero's discards are 3h7c.


thanks for the corrections on my math, dunno what to say, i never got my grade 12