4 to the nut flush - Page 3

#21 07-30-2005, 04:01 PM

Thanks very much. Very thoughtful. I'm going to think about it, let my head explode, and then attempt some math.

#22 07-30-2005, 04:25 PM

[ QUOTE ]
Okay, I started out hoping to do some EV analysis of this problem, but I've found that there are too many assumptions that need to be made and the final result wouldn't really be indicitave of anything. So instead I'm going to use Pokerstove equity calculations to try and show why the Ace outs really don't mean that much to us.

That said, some assumptions still have to be made. I'm going to assume SB has KJ or QJ and UTG has J9 for 2 pair. This assumption is debatable and is clearly not perfect, but given the action I think this is reasonable. The "randomiser" will be CO, who could be holding anything. One time I'll give him a range of suited connector hands, and in another I'll give him specifically AK/A6 (which would render our A outs worthless most of the time), as well as AA.

Simulation 1
Code:<hr /><pre>
3,660,480 games 1.515 secs 2,416,158 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.0570 % [ 00.35 00.00 ] { AsTs }
Hand 2: 08.3255 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 45.8619 % [ 00.46 00.00 ] { J9s, J9o }
Hand 4: 10.7556 % [ 00.11 00.00 ] { T8s, 98s-97s, 87s-86s, 76s-75s, 65s-64s, 54s }</pre><hr />

Simulation 2
Code:<hr /><pre>
2,302,560 games 0.969 secs 2,376,222 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.9336 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.5860 % [ 00.07 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 49.6427 % [ 00.49 00.00 ] { J9s, J9o }
Hand 4: 07.8377 % [ 00.08 00.00 ] { AKs, A6s, AKo, A6o }</pre><hr />

You can see here that our equity barely moves.

It doesn't really matter what range of hands I give my opponents, in fact. Our equity hardly changes at all. Here is CO with a very oddly played AA, which destroys any hope of our As being any good:

Simulation 3
Code:<hr /><pre>
354,240 games 0.140 secs 2,530,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.8323 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.8506 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 40.8537 % [ 00.41 00.00 ] { J9s, J9o }
Hand 4: 16.4634 % [ 00.16 00.00 ] { AA }
</pre><hr />

In this case, we've only lost 0.2% of equity against the hand which hurts our ace outs the most (partly because there are less aces for us to catch, and also because if we do get one, it's certainly not good). That is a tiny amount of equity.

The only hands which significantly impact our equity here are JJ, 99 and 66, because they can boat up to beat our flush some of the time:

Simulation 4
Code:<hr /><pre>
118,080 games 0.063 secs 1,874,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 30.9604 % [ 00.31 00.00 ] { AsTs }
Hand 2: 02.3780 % [ 00.02 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 04.5122 % [ 00.05 00.00 ] { J9s, J9o }
Hand 4: 62.1494 % [ 00.62 00.00 ] { JJ, 99, 66 }</pre><hr />

So what happens to our equity when SB and CO both fold to our well-timed turn raise? This is a fairly optimistic view of the situation, but lets look to see what knocking these two players out really does for our equity (lets assume that they disappear from the flop too for some reason, since the turn is not relevant for this decision):

Simulation 5
Code:<hr /><pre>
8,910 games 0.005 secs 1,782,000 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.6465 % [ 00.35 00.00 ] { AsTs }
Hand 2: 65.3535 % [ 00.65 00.00 ] { J9s, J9o }</pre><hr />

Our equity actually goes down. We have gained nothing from knocking the weaker hands out, but we've stopped them from putting money into our pot. We will only gain equity if UTG does indeed hold something weaker than 2 pair, but only if that something also dominates our ace. This parlay is going to be rare indeed.

Conclusion
What all of this means is, we don't even want AA to fold in this spot! Our As do not impact our chance of winning the hand in any significant way given these range of holdings. The only hands that improve our chance of winning this hand by having them fold are exactly the hands JJ, 99 and 66. These hands aren't folding any time soon.

I don't need to do the EV calculations here since the equities are almost exactly the same. It can be seen by inspection that every bet missed on this flop is a straight up loss in EV.

Note that if UTG is playing something less than 2 pair, then our equity can increase slightly by folding out other opponents. I don't think this is going to happen here very often though.

Just so you think I'm not crazy, I'll add one more simulation with two completely random hands. Our equity doesn't go down the slightest (infact it increases). It is clear to see that we have no interest in folding any of these hands.

Simulation 6
Code:<hr /><pre>
98,849,717 games 72.750 secs 1,358,758 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.9402 % [ 00.36 00.00 ] { AsTs }
Hand 2: 06.0087 % [ 00.06 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 34.9817 % [ 00.35 00.00 ] { J9s, J9o }
Hand 4: 12.5630 % [ 00.13 00.00 ] { AA }
Hand 5: 05.8262 % [ 00.05 00.00 ] { random }
Hand 6: 04.6802 % [ 00.04 00.00 ] { random }</pre><hr />

Well, that was a long post. Congrats if you got to the bottom of it. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

I am wondering about your assumptions of hands. The comparison hand that you used in Simulation 5 (where only one hand is left) was a 2-pair hand. That could be a fair assumption -- with so many bets, it doesn't seem unreasonable. But, isn't it just as reasonable to assume that the best hand we are facing after we get 1-2 hands to fold (itself a big assumption) is not 2-pair, but is a made pair and/or a straight or flush draw? If so, here is an example of a calculation:

pokenum -h as ts - qd 9d - 7c 8d -- jd 6s 9s
Holdem Hi: 903 enumerated boards containing 9s 6s Jd
cards win %win lose %lose tie %tie EV
As Ts 408 45.18 495 54.82 0 0.00 0.452
Qd 9d 339 37.54 564 62.46 0 0.00 0.375
7c 8d 156 17.28 747 82.72 0 0.00 0.173

If this was the scenario, then our EV has increased substantially just by having one hand fold on the turn, right??? And then wouldn't it be correct to try to get one hand to fold in this large pot?

By the way, assuming for the sake of argument that it is correct to try to or care about getting others to fold here, do you agree that the best way to accomplish it here is to wait for the turn?

TALLBrad · #23 07-30-2005, 04:28 PM

My thinking on the flop is similar to yours, now with the situation of calling 2 or raising to 3:
Drawing hand
9 outs to the Nut Flush
1 out for the backdoor straight
1 (discounted) out for the 3 remaining aces
11 total outs, meaning you need 3.7 or so to call
18 SB in the pot to you:

I believe this situation calls for a Raise! You have strength, might even be favored to win the pot at the moment, play to that strength. Then re-evaluate on the turn, in particular if you don't hit one of your cards.

Just to note, the weak tighty in me would probably call in the 30 second realm of the on-line decision making process.

Brad.

#24 07-30-2005, 04:51 PM

[ QUOTE ]
[ QUOTE ]
Okay, I started out hoping to do some EV analysis of this problem, but I've found that there are too many assumptions that need to be made and the final result wouldn't really be indicitave of anything. So instead I'm going to use Pokerstove equity calculations to try and show why the Ace outs really don't mean that much to us.

That said, some assumptions still have to be made. I'm going to assume SB has KJ or QJ and UTG has J9 for 2 pair. This assumption is debatable and is clearly not perfect, but given the action I think this is reasonable. The "randomiser" will be CO, who could be holding anything. One time I'll give him a range of suited connector hands, and in another I'll give him specifically AK/A6 (which would render our A outs worthless most of the time), as well as AA.

Simulation 1
Code:<hr /><pre>
3,660,480 games 1.515 secs 2,416,158 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.0570 % [ 00.35 00.00 ] { AsTs }
Hand 2: 08.3255 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 45.8619 % [ 00.46 00.00 ] { J9s, J9o }
Hand 4: 10.7556 % [ 00.11 00.00 ] { T8s, 98s-97s, 87s-86s, 76s-75s, 65s-64s, 54s }</pre><hr />

Simulation 2
Code:<hr /><pre>
2,302,560 games 0.969 secs 2,376,222 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.9336 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.5860 % [ 00.07 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 49.6427 % [ 00.49 00.00 ] { J9s, J9o }
Hand 4: 07.8377 % [ 00.08 00.00 ] { AKs, A6s, AKo, A6o }</pre><hr />

You can see here that our equity barely moves.

It doesn't really matter what range of hands I give my opponents, in fact. Our equity hardly changes at all. Here is CO with a very oddly played AA, which destroys any hope of our As being any good:

Simulation 3
Code:<hr /><pre>
354,240 games 0.140 secs 2,530,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.8323 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.8506 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 40.8537 % [ 00.41 00.00 ] { J9s, J9o }
Hand 4: 16.4634 % [ 00.16 00.00 ] { AA }
</pre><hr />

In this case, we've only lost 0.2% of equity against the hand which hurts our ace outs the most (partly because there are less aces for us to catch, and also because if we do get one, it's certainly not good). That is a tiny amount of equity.

The only hands which significantly impact our equity here are JJ, 99 and 66, because they can boat up to beat our flush some of the time:

Simulation 4
Code:<hr /><pre>
118,080 games 0.063 secs 1,874,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 30.9604 % [ 00.31 00.00 ] { AsTs }
Hand 2: 02.3780 % [ 00.02 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 04.5122 % [ 00.05 00.00 ] { J9s, J9o }
Hand 4: 62.1494 % [ 00.62 00.00 ] { JJ, 99, 66 }</pre><hr />

So what happens to our equity when SB and CO both fold to our well-timed turn raise? This is a fairly optimistic view of the situation, but lets look to see what knocking these two players out really does for our equity (lets assume that they disappear from the flop too for some reason, since the turn is not relevant for this decision):

Simulation 5
Code:<hr /><pre>
8,910 games 0.005 secs 1,782,000 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.6465 % [ 00.35 00.00 ] { AsTs }
Hand 2: 65.3535 % [ 00.65 00.00 ] { J9s, J9o }</pre><hr />

Our equity actually goes down. We have gained nothing from knocking the weaker hands out, but we've stopped them from putting money into our pot. We will only gain equity if UTG does indeed hold something weaker than 2 pair, but only if that something also dominates our ace. This parlay is going to be rare indeed.

Conclusion
What all of this means is, we don't even want AA to fold in this spot! Our As do not impact our chance of winning the hand in any significant way given these range of holdings. The only hands that improve our chance of winning this hand by having them fold are exactly the hands JJ, 99 and 66. These hands aren't folding any time soon.

I don't need to do the EV calculations here since the equities are almost exactly the same. It can be seen by inspection that every bet missed on this flop is a straight up loss in EV.

Note that if UTG is playing something less than 2 pair, then our equity can increase slightly by folding out other opponents. I don't think this is going to happen here very often though.

Just so you think I'm not crazy, I'll add one more simulation with two completely random hands. Our equity doesn't go down the slightest (infact it increases). It is clear to see that we have no interest in folding any of these hands.

Simulation 6
Code:<hr /><pre>
98,849,717 games 72.750 secs 1,358,758 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.9402 % [ 00.36 00.00 ] { AsTs }
Hand 2: 06.0087 % [ 00.06 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 34.9817 % [ 00.35 00.00 ] { J9s, J9o }
Hand 4: 12.5630 % [ 00.13 00.00 ] { AA }
Hand 5: 05.8262 % [ 00.05 00.00 ] { random }
Hand 6: 04.6802 % [ 00.04 00.00 ] { random }</pre><hr />

Well, that was a long post. Congrats if you got to the bottom of it. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

I am wondering about your assumptions of hands. The comparison hand that you used in Simulation 5 (where only one hand is left) was a 2-pair hand. That could be a fair assumption -- with so many bets, it doesn't seem unreasonable. But, isn't it just as reasonable to assume that the best hand we are facing after we get 1-2 hands to fold (itself a big assumption) is not 2-pair, but is a made pair and/or a straight or flush draw? If so, here is an example of a calculation:

pokenum -h as ts - qd 9d - 7c 8d -- jd 6s 9s
Holdem Hi: 903 enumerated boards containing 9s 6s Jd
cards win %win lose %lose tie %tie EV
As Ts 408 45.18 495 54.82 0 0.00 0.452
Qd 9d 339 37.54 564 62.46 0 0.00 0.375
7c 8d 156 17.28 747 82.72 0 0.00 0.173

If this was the scenario, then our EV has increased substantially just by having one hand fold on the turn, right??? And then wouldn't it be correct to try to get one hand to fold in this large pot?

By the way, assuming for the sake of argument that it is correct to try to or care about getting others to fold here, do you agree that the best way to accomplish it here is to wait for the turn?

[/ QUOTE ]

I've been thinking alot about this, and I may finally have a grip on what I'm trying to say, and it's this:

Bottom line here: The pot is going to end up at about 18 BB, so if someone stays in the pot and beats you more than 1 in 18 times (5.5%), when they otherwise would have folded had you protected your hand correctly, then you have made a huge mistake. Based on the calculation I just did, I think that there is a significant enough chance (more than 5.5%, probably about 10% -- by comparing the Equity analysis you did to the one I did) that a hand allowed to compete, which should have been made to fold, will beat you and take the pot.

In contrast, losing individual bets on any particular round would be a small mistake.

Thus, in my mind the overriding question here is still how best to protect my hand -- is it by raising on the flop or on the turn?

bozlax · #25 07-30-2005, 05:44 PM

You've already got one cold-caller. I call this and try to not blow SB out of the water.

bozlax · #26 07-30-2005, 05:46 PM

[ QUOTE ]
Congrats if you got to the bottom of it. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

I got there, I just didn't read any of it.

TomBrooks · #27 07-30-2005, 05:52 PM

Three bet, my boy, three bet.

TomBrooks · #28 07-30-2005, 05:59 PM

[ QUOTE ]
You've already got one cold-caller. I call this and try to not blow SB out of the water.

[/ QUOTE ]
True that you wouldn't want SB to fold. I'd guess the risk of that may be more than offset by the possibility of getting a free card, and may help avoid having to invest two bets in the turn if the turn betting were to follow the same pattern as that on the flop.

Guthrie · #29 07-30-2005, 06:03 PM

Wow, a lot of excellent analysis, but I only had a few seconds, so I called. I felt certain that UTG had at least a pair, and based on his previous play in just one orbit, there was no way I was pushing him off. If I made my flush, and the board didn't pair, I wanted two opponents instead of one anyway, and felt sure they would continue to donate. If I missed my flush I didn't want to depend on spiking an ace and hoping nobody had two pair or caught a straight. I easily had odds to call all the way to the river, but knew I was beat at the end.

Paradise Poker 0.25/0.50 Hold'em (8 handed) converter

Preflop: Hero is Button with A[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/spade.gif[/img].
UTG calls, 1 fold, MP1 calls, MP2 calls, CO calls, Hero raises, SB calls, 1 fold, UTG calls, MP1 calls, MP2 calls, CO calls.

Flop: (13 SB) J[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/spade.gif[/img] (6 players)
SB bets, UTG raises, MP1 folds, MP2 folds, CO calls, Hero calls, SB calls.

Turn: (10.50 BB) 3[img]/images/graemlins/diamond.gif[/img] (4 players)
SB folds, UTG bets, CO calls, Hero calls.

River: (13.50 BB) 4[img]/images/graemlins/heart.gif[/img] (3 players)
UTG bets, CO calls, Hero folds.

Final Pot: 15.50 BB

Results in white below: 
UTG has 9d Jh (two pair, jacks and nines).
CO has Js Qc (one pair, jacks).
Outcome: UTG wins 15.50 BB.

#30 07-30-2005, 07:09 PM

[ QUOTE ]
Okay, I started out hoping to do some EV analysis of this problem, but I've found that there are too many assumptions that need to be made and the final result wouldn't really be indicitave of anything. So instead I'm going to use Pokerstove equity calculations to try and show why the Ace outs really don't mean that much to us.

That said, some assumptions still have to be made. I'm going to assume SB has KJ or QJ and UTG has J9 for 2 pair. This assumption is debatable and is clearly not perfect, but given the action I think this is reasonable. The "randomiser" will be CO, who could be holding anything. One time I'll give him a range of suited connector hands, and in another I'll give him specifically AK/A6 (which would render our A outs worthless most of the time), as well as AA.

Simulation 1
Code:<hr /><pre>
3,660,480 games 1.515 secs 2,416,158 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.0570 % [ 00.35 00.00 ] { AsTs }
Hand 2: 08.3255 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 45.8619 % [ 00.46 00.00 ] { J9s, J9o }
Hand 4: 10.7556 % [ 00.11 00.00 ] { T8s, 98s-97s, 87s-86s, 76s-75s, 65s-64s, 54s }</pre><hr />

Simulation 2
Code:<hr /><pre>
2,302,560 games 0.969 secs 2,376,222 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.9336 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.5860 % [ 00.07 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 49.6427 % [ 00.49 00.00 ] { J9s, J9o }
Hand 4: 07.8377 % [ 00.08 00.00 ] { AKs, A6s, AKo, A6o }</pre><hr />

You can see here that our equity barely moves.

It doesn't really matter what range of hands I give my opponents, in fact. Our equity hardly changes at all. Here is CO with a very oddly played AA, which destroys any hope of our As being any good:

Simulation 3
Code:<hr /><pre>
354,240 games 0.140 secs 2,530,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.8323 % [ 00.35 00.00 ] { AsTs }
Hand 2: 07.8506 % [ 00.08 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 40.8537 % [ 00.41 00.00 ] { J9s, J9o }
Hand 4: 16.4634 % [ 00.16 00.00 ] { AA }
</pre><hr />

In this case, we've only lost 0.2% of equity against the hand which hurts our ace outs the most (partly because there are less aces for us to catch, and also because if we do get one, it's certainly not good). That is a tiny amount of equity.

The only hands which significantly impact our equity here are JJ, 99 and 66, because they can boat up to beat our flush some of the time:

Simulation 4
Code:<hr /><pre>
118,080 games 0.063 secs 1,874,285 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 30.9604 % [ 00.31 00.00 ] { AsTs }
Hand 2: 02.3780 % [ 00.02 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 04.5122 % [ 00.05 00.00 ] { J9s, J9o }
Hand 4: 62.1494 % [ 00.62 00.00 ] { JJ, 99, 66 }</pre><hr />

So what happens to our equity when SB and CO both fold to our well-timed turn raise? This is a fairly optimistic view of the situation, but lets look to see what knocking these two players out really does for our equity (lets assume that they disappear from the flop too for some reason, since the turn is not relevant for this decision):

Simulation 5
Code:<hr /><pre>
8,910 games 0.005 secs 1,782,000 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 34.6465 % [ 00.35 00.00 ] { AsTs }
Hand 2: 65.3535 % [ 00.65 00.00 ] { J9s, J9o }</pre><hr />

Our equity actually goes down. We have gained nothing from knocking the weaker hands out, but we've stopped them from putting money into our pot. We will only gain equity if UTG does indeed hold something weaker than 2 pair, but only if that something also dominates our ace. This parlay is going to be rare indeed.

Conclusion
What all of this means is, we don't even want AA to fold in this spot! Our As do not impact our chance of winning the hand in any significant way given these range of holdings. The only hands that improve our chance of winning this hand by having them fold are exactly the hands JJ, 99 and 66. These hands aren't folding any time soon.

I don't need to do the EV calculations here since the equities are almost exactly the same. It can be seen by inspection that every bet missed on this flop is a straight up loss in EV.

Note that if UTG is playing something less than 2 pair, then our equity can increase slightly by folding out other opponents. I don't think this is going to happen here very often though.

Just so you think I'm not crazy, I'll add one more simulation with two completely random hands. Our equity doesn't go down the slightest (infact it increases). It is clear to see that we have no interest in folding any of these hands.

Simulation 6
Code:<hr /><pre>
98,849,717 games 72.750 secs 1,358,758 games/sec
Board: Jd 6s 9s
equity (%) win (%) / tie (%)
Hand 1: 35.9402 % [ 00.36 00.00 ] { AsTs }
Hand 2: 06.0087 % [ 00.06 00.00 ] { KJs, QJs, KJo, QJo }
Hand 3: 34.9817 % [ 00.35 00.00 ] { J9s, J9o }
Hand 4: 12.5630 % [ 00.13 00.00 ] { AA }
Hand 5: 05.8262 % [ 00.05 00.00 ] { random }
Hand 6: 04.6802 % [ 00.04 00.00 ] { random }</pre><hr />

Well, that was a long post. Congrats if you got to the bottom of it. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

Great post and great read. Not to be too results oriented, but you were right in that actual situation. Here's how he stood at the flop (assuming SB would fold, as he actually did):

pokenum -h as ts - 9d jh - js qc -- jd 6s 9s
Holdem Hi: 903 enumerated boards containing 9s 6s Jd
cards win %win lose %lose tie %tie EV
As Ts 327 36.21 576 63.79 0 0.00 0.362
9d Jh 496 54.93 402 44.52 5 0.55 0.552
Js Qc 75 8.31 823 91.14 5 0.55 0.086