ChuckTs
Legend
Silver Level
Well close enough 
However right you get it, it's just to degrees of how dead you're drawing.
The example (from here) says this:
Your ten opponents hold AA through JJ, 66, 33, 78s, 45s and 57s. Flop is 9c 6s 3d (suits don't matter, but it's rainbow).
In that case you are technically ahead atm, but you're drawing to one out twice since any other card will kill you. A ten or a deuce will give you additional outs for a FH (T or 2 would fill the FH; others would only give quads to someone else). The case 9 will of course win it for you assuming noone makes a backdoor straight flush
However right you get it, it's just to degrees of how dead you're drawing.
The example (from here) says this:
Your ten opponents hold AA through JJ, 66, 33, 78s, 45s and 57s. Flop is 9c 6s 3d (suits don't matter, but it's rainbow).
In that case you are technically ahead atm, but you're drawing to one out twice since any other card will kill you. A ten or a deuce will give you additional outs for a FH (T or 2 would fill the FH; others would only give quads to someone else). The case 9 will of course win it for you assuming noone makes a backdoor straight flush
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Hard2Handle
Enthusiast
Silver Level
Well in there were 10 players then this would be the worse scenerio.
Flop 9-5-4
1-5 hold tens through aces.
6 holds 55
7 holds 44
8 holds 67
9 holds A3
You being the 10th holding 99.
Your only safe cards would be the case 9 and a 5 or 4 if it didn't hit twice.
Flop 9-5-4
1-5 hold tens through aces.
6 holds 55
7 holds 44
8 holds 67
9 holds A3
You being the 10th holding 99.
Your only safe cards would be the case 9 and a 5 or 4 if it didn't hit twice.
vanquish
Legend
Silver Level
Well close enough
However right you get it, it's just to degrees of how dead you're drawing.
The example (from here) says this:
Your ten opponents hold AA through JJ, 66, 33, 78s, 45s and 57s. Flop is 9c 6s 3d (suits don't matter, but it's rainbow).
In that case you are technically ahead atm, but you're drawing to one out twice since any other card will kill you. A ten or a deuce will give you additional outs for a FH (T or 2 would fill the FH; others would only give quads to someone else). The case 9 will of course win it for you assuming noone makes a backdoor straight flush
Bleh I brought this up a while ago actually (top set is actually drawing to quads - only way of winning). https://www.cardschat.com/forum/cash-game-hand-analysis-50/nuts-but-still-behind-92787/
B
Bentheman87
Visionary
Silver Level
Yeah, dont fold a set. Sure there's a possible straight, but its very unlucky. As Dan Harrington says, if your set gets outflopped youre supposed to lose a lot of money. And several times I have flopped a straight on the flop and got all in against a player who flopped a set, and he wins with a full house when the board pairs on the turn or river.
K_Kahne_Fan
Legend
Silver Level
Easy, you fold when you're playing on (name your site), because it's rigged! They're all rigged!! It's a conspiracy to take my money. They've built these sites with $?m(?) just to wait for me to have a set of 9's so they could bust it and take my $5 buy-in
Cheetah
Visionary
Silver Level
I am answering the more restricted version of this question using your example, Chuck.
The answer is CALL!
Let me first make a few qualifications:
- We ignore tournament bubble effects where you might fold a +EV hand to get in the money
- Implied odds usually matter. Since there are no chip stacks, I have assumed the worst case scenario. Say the game is 1/2c, We are in the big blind, and everyone pushes all-in for $1 million. Do we call $1 million or not? Pot odds = implied odds = 9:1 (or 10% win rate)
I devised a visual representation of the calculation of our odds because if I use combinatorics, most people would fall asleep and probably not believe me anyway
.Before explaining the the picture, let me appeal to your intuition. We have 99, top set, one of our opponents has AA. Considering just that one opponent, do we have +EV with respect to that one opponent? I am sure most of you will say "yes". And indeed, we already have a set, they must hit their set. Even when they hit, we still have one out left to outdraw them.
The argument that there are so many of them that we must be behind is not valid because if we are ahead of each one of them, then we are ahead of them even collectively in terms of +EV. We could even be behind some of them (in terms of EV), and still be ahead overall.
I am not answering the bigger question whether there is ANY combination of hands that results in -EV for us. I suspect there isn't any.
But what follows is a proof that the example provided by Chuck is a clear call.
Basically, we must count how many times we win and lose. Now look at the picture. I have summarized the situation (flop, hero, other 9 players).
There are 29 cards left in the deck because we have 10 players (20 cards) and the flop(3 cards). Therefore, we have 29 possible turn cards. Clearly, after the turn, we have 28 possible river cards. That makes a total of 29 x 28 possible turn/river combinations = 812
In order for us to have a +EV, we need at least 10% win rate, which means we need to win at least 82 of these 812 combinations.
On the attached picture, the turn card is represented in blue. To the left of the turn card is how many of those cards we have left in the deck.
The columns represent the river card. The numbers inside this matrix represent how many river cards of that type are left in the deck.
The green areas represent our winning combinations. When we calculate our winning combinations, we arrive at 96 which is more than 82.
Therefore, we MUST call!
If you have any questions, let me know.
P.S. The original example says that the non-paired players have suited cards. This is irrelevant to us sine we can only beat their str8s with FHs.
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zachvac
Legend
Silver Level
Sorry, but the answer to the original question is plain wrong. I ran a pokerstove analysis on it and you are 11% to win in a 10-way pot. Enough to call even without the money in the pot PF. You are not the favorite, but even if the bet was infinite with respect to money in the pot, you make the call. A worse scenario comes when rather than AA, he has A9. Now you are under 5% to win, because rather than drawing to the 9, you're drawing to 22, TT, or AA, 11 outs then 1, 2, or 3 outs, which is worse than the draw to 9 outs, if you hit one already having the win, if not drawing to 4 outs.
My new challenge (not sure if it's possible):
Give me a 10-way hand that is the nuts postflop yet actually drawing dead. THAT would make for an interesting hand, although I'm not sure it's possible. I'm guessing if it is possible you don't have a great hand but everyone else has massive draws. I haven't been able to think of one, but it could be possible.
My new challenge (not sure if it's possible):
Give me a 10-way hand that is the nuts postflop yet actually drawing dead. THAT would make for an interesting hand, although I'm not sure it's possible. I'm guessing if it is possible you don't have a great hand but everyone else has massive draws. I haven't been able to think of one, but it could be possible.
zachvac
Legend
Silver Level
I wrote my response before I saw this, and he basically said some of what I said, but I have a question about whether the end of this is right. If we are beating every opponent head on (including draws and such, not just at this moment), are we guaranteed to be +ev? In fact, this is definitely false, as we'll see in a second with my example (AA having A9 instead).I am answering the more restricted version of this question using your example, Chuck.
The answer is CALL!
Let me first make a few qualifications:I became very suspicious reading this example as something one should fold. Let's realize that we are not looking to be "favorite" to win. We are looking for +EV! If we win, we win 9 units. If we lose, we lose only 1 unit. So if we are better than 9:1 dog, we must call. Another way to say this is we must win more than 10% of the time to make it a profitable call.
- We ignore tournament bubble effects where you might fold a +EV hand to get in the money
- Implied odds usually matter. Since there are no chip stacks, I have assumed the worst case scenario. Say the game is 1/2c, We are in the big blind, and everyone pushes all-in for $1 million. Do we call $1 million or not? Pot odds = implied odds = 9:1 (or 10% win rate)
I devised a visual representation of the calculation of our odds because if I use combinatorics, most people would fall asleep and probably not believe me anyway
Before explaining the the picture, let me appeal to your intuition. We have 99, top set, one of our opponents has AA. Considering just that one opponent, do we have +EV with respect to that one opponent? I am sure most of you will say "yes". And indeed, we already have a set, they must hit their set. Even when they hit, we still have one out left to outdraw them.
Mostly right, but it doesn't matter if we're ahead of each of them, it matters if overall we are 10% to win each hand or better. That's all that matters. Getting 2nd place every hand doesn't win any money, and if we can beat all but one in most situations (which I believe will be the case in my example), we still beat everyone the majority of the time, but the small majority of the time they beat us, they beat everyone.
As I mentioned, there is.
Nice analysis, and correct about the suited not mattering. Trips cannot win the hand, any hand we have that will win the hand will also beat a flush, thus we can ignore the flush (which further emphasizes the fact that comparing against single opponents, where the flush WILL impact our head-to-head percentage, it does NOT impact our overall percentage thus we can ignore it).
So about that example, where AA has A9 instead. Let's look at each head to head.
A9 vs. 99, flop=963, he only wins with running aces, we win every other time, we have him dominated.
KK, QQ, and JJ vs. 99, He has 2 draws to 2 outs, we're the clear favorite
66, 33 vs. 99, he has 2 draws to 1 out, we're the clear favorite again
87 vs. 99, this is the best hand against ours, as he is drawing to 8 outs, has 2 shots to do it, plus if the suited cards match one of the board's suits he also has runner-runner flush draw. But we have re-draws of 6 outs if he hits the straight (another of whichever card completes the straight, or a 6 or 3). But although he has a good draw, and he may have odds to call in a hand against us if we don't bet big enough compared to the pot, he is still obviously the underdog here, as simply drawing to 8 outs even with 2 cards to come is not greater than 50% (1-(37/45)(36/44)) = 32.7%. Runner-runner draws (also some re-draws for us) are not enough to make up the difference and make them a favorite
45 vs. 99, pretty much identical to the above with different numbers to straight, same concepts though, and should be identical percentage.
75 vs. 99, again, pretty much the same percentages, this time it's not a straightforward open-ended draw, but there are still 2 cards to fill the straight, thus a very similar percentage. We are again the favorite.
But because we have such a strong hand, we end up in 2nd place a lot. So although we're ahead of every hand and the majority of the time we beat each individual hand, we end up in 2nd place a lot, thus counting for us beating 8 of our 9 opponents yet winning 0% of the pot. So we come away with 4.926% to win (according to pokerstove) and we would NOT call if we saw A9 flipped over rather than AA.
Cheetah
Visionary
Silver Level
King, I am glad I cleared that up for you. No poker player is complete without knowing how to play in this situation.
Cheetah
Visionary
Silver Level
zachvac, you are correct. If we substitute AA with A9, we are only 4.93% to win. I am including the visual calculation in that case.
BTW, who is that donkey that went all-in with A9? :laugh:
Here is an excercise for the truly twisted minds: How much worse can we make this top set situation? :evil:
BTW, who is that donkey that went all-in with A9? :laugh:
Here is an excercise for the truly twisted minds: How much worse can we make this top set situation? :evil:
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Cheetah
Visionary
Silver Level
I don't think this one qualifies. 999 is a pair of nines with 9 kicker.
Besides, the setup is such that you know you have the nuts on the flop even if you don't know their hole cards.
zachvac
Legend
Silver Level
but you don't have top set in this situation. Set=2 in your hand, one on the board, right?
But this provides the foundation for the answer as to how it's possible to have the best hand (although it is not the nuts) and be drawing absolutely dead.
board = 333
your hand = 22
other hands: AK, QJ, T9, 87, 65, A2, A4
I think the hands AK - 65 are obvious why they're needed, a card above a 3 comes and someone has the higher boat. The A2 is needed just so that you can not hit runner runner quads and the A4 provides 2 purposes, taking away the last A (so the turn and river aren't 3-A, splitting the pot as everyone has quads A kicker) and taking the 4 so that running 4's doesn't split the pot. So at this point you have the best hand, 3s full of 2s. But the next card will put you behind no matter what, unless it's a 2, which keeps your best hand at 3s full of 2s (no poker hand called double trips
) and the last card, since there are no 2s left will either give someone a higher boat or else put quads on the board splitting the pot between the people with A high kicker to the quads.