Big Draw Theory

[simo_8ball 0]

Pot Limit Holdem Ring gameBlinds: $25/$502 playersStack sizes:Button: $10,000BB: $10,000Pre-flop: (5 players) Dealt to Button A A Dealt to BB 8 9 :heart:Button calls dark, BB checks dark. The cards are then turned face up.Flop: J T 2 ($100, 2 players)

Board: Jh Th 2cDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 	48.384%	  48.38% 	00.00% 			   479 			0.00   { AsAh }Hand 1: 	51.616%	  51.62% 	00.00% 			   511 			0.00   { 9h8h }

This is pot limit.1) Which hand would you prefer?2) How should the action go, and why?3) If BB bets pot, what should the Button do?

[Canadianpoker83 0]

Well if i had to choose i'd say AA only because if a heart hits the turn we still have a chance to re-draw to the higher flush. However the other hand is so pretty. As we all know to close to call.

[David_Nicoson 1]

I think we're going to need these numbers.

44  games	 0.005 secs	 8,800  games/secBoard: Jh Th 2c QsDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 06.818%	  06.82% 	00.00% 				 3 			0.00   { AhAs }Hand 1: 93.182%	  93.18% 	00.00% 				41 			0.00   { 9h8h }---  44  games	 0.005 secs	 8,800  games/secBoard: Jh Th 2c 4hDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 11.364%	  11.36% 	00.00% 				 5 			0.00   { AhAs }Hand 1: 88.636%	  88.64% 	00.00% 				39 			0.00   { 9h8h }---  44  games	 0.005 secs	 8,800  games/secBoard: Jh Th 2c 5sDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 68.182%	  68.18% 	00.00% 				30 			0.00   { AhAs }Hand 1: 31.818%	  31.82% 	00.00% 				14 			0.00   { 9h8h }---

[CobaltBlue 662]

1) Which hand would you prefer?2) How should the action go, and why?3) If BB bets pot, what should the Button do?

1) Don't have much preference either way. That said, my first instinct is to go with the flop favorite, but upon reflection, I think the AA will be easier to play.2) The BB should bet the pot on the flop, and the Button should call. On the turn, the BB should check, the Button should bet as large of an amount as the BB will call. The action on the river is irrelevant.3) See above.(I'm fairly confident in my answers as they seem to recall a recent CP article that I read...but I'm not entirely sure.)

[psujohn 0]

I think the monster draw loses some value in a pot limit vs a no limit game. In no limit our ideal situation with the monster draw is to get a bunch of money in the middle and then shove over the pair and have him fold. Ideally we get the pair to put in as much as possible that he can still fold when we shove. Though the monster draw is a favorite on the flop it still gets more value by driving out the big pair.The big pair on the other hand gains value simply because it can guarantee it sees the turn where the equity changes drastically and the big pair is generally unable to get the monster draw to fold on the flop for any amount.

[simo_8ball 0]

Hmm. I've just thought of something that complicates this example further. I may have to reconsider the solution.

[mtdesmoines 3]

This is pot limit.

I go broke with either hand on the flop here in NL.Pot limit can get as big as NL if we both pot the flop.

[simo_8ball 0]

I go broke with either hand on the flop here in NL.Pot limit can get as big as NL if we both pot the flop.

Both hands are face up remember.

[simo_8ball 0]

Pot Limit Holdem Ring gameBlinds: $25/$502 playersStack sizes:Button: $450BB: $450Pre-flop: (5 players) Dealt to BB A A Dealt to Button 8 9 :heart:Button calls dark, BB checks dark. The cards are then turned face up.Flop: J T 2 ($100, 2 players)Now what should the action be in the following 2 cases? The draw is acting first now, and they have $400 each left (a pot bet and pot raise).

[krup24 0]

i wonder what changing the Ah to Ac does in your first example?i also wonder what this one would be:AhAd7c8cFlop 5c 6c Xi would feel way more comfortable in this one

[mtdesmoines 3]

I go broke with either hand on the flop here in NL.Pot limit can get as big as NL if we both pot the flop.

Both hands are face up remember.

Yah, I know. Face up ... I would fold the AA in the face of that draw. What changes it marginally in PL v. NL is that we can't pay to see both cards in PL and if we see a blank on the turn, maybe we can are tempted to get away in the face of a PSB with one to come ...

[Frez 0]

With the cards face up, I would prefer the better hand obv.As for how the action should go, BB is first to act and he knows he is a favourite, so he should pot. Button has to call, because even though he knows he is behind he still has enough equity to call in that spot.The flop play in this PL scenario is dead easy. Actually, so is the turn I think. If BB hits he pots again, if he misses he has to c/f because button must pot. When he does BB is getting only 2-1 on a 3.1-1 chance, with exactly ZERO implied odds since the hands are face up.Hmmm, that makes me think about the flop again. Basically this is a 4 card game, because the river will have no betting action. On the flop BB is helped by 14/45 cards, therefor he is more likely to miss than make it. Looking at it that way, the AA is a favourite and he should bet/raise because he is ahead. If BB calls and hits on the turn, Button can fold because he is way behind. But if the turn misses the BB, button can bet/raise again and as I said above, BB would be making a mistake to call.The fact that it's PL makes the AA play easier, so now I say that's the hand I would rather play. If it was NL the only play is for BB to shove and Button to fold. Any smaller bet by BB prices the Button in.

[simo_8ball 0]

Hmmm, that makes me think about the flop again. Basically this is a 4 card game, because the river will have no betting action. On the flop BB is helped by 14/45 cards, therefor he is more likely to miss than make it. Looking at it that way, the AA is a favourite and he should bet/raise because he is ahead. If BB calls and hits on the turn, Button can fold because he is way behind. But if the turn misses the BB, button can bet/raise again and as I said above, BB would be making a mistake to call.The fact that it's PL makes the AA play easier, so now I say that's the hand I would rather play. If it was NL the only play is for BB to shove and Button to fold. Any smaller bet by BB prices the Button in.

Now you're getting there.It's not as simple as "the draw is a favourite so he should bet/raise".

[Acid_Knight 2]

There is defintely an article pertaining to almost this exact situation that was written in cardplayer a ways back and what was the most EV way to play it.In practice, I'd almost always want the 89hh unless the hands are face up. I can play it like the nuts and AA will sometimes fold. If both hands are exposed, then someone should find the cardplayer article, though I can't remember for the life of me who wrote it.

[Sheiky 0]

This is quite clearly AA no?In NL it's different i'm guessing, but in PL if the button does the right thing and calls a flop bet he doesn't have to put any money in on the turn if the BB hits his 14 outs, and if he missed he can profitably bet/call the BB with only the river to come.Any play after that just sends my head into a spin.Continuing the theme of theory questions, here's one i found on 2+2.The situation: First hand of the WSOP ME, you're in the SB and it's folded to you, the BB is Phil Helmuth who has decided to turn up early this year. Assuming that Phil Helmuth will only call an all in with pocket aces, which hand is best to move in with, A5o or 89s? This is with 10k stacks 25/50 blinds.

[simo_8ball 0]

First hand of the WSOP ME, you're in the SB and it's folded to you, the BB is Phil Helmuth who has decided to turn up early this year. Assuming that Phil Helmuth will only call an all in with pocket aces, which hand is best to move in with, A5o or 89s?

A5o. Not close. The card removal effects of the A5o outweigh the added showdown equity of the 89s. You get called 1/2 as often when you have A5o.

[Sheiky 0]

Smartass...

[simo_8ball 0]

There is defintely an article pertaining to almost this exact situation that was written in cardplayer a ways back and what was the most EV way to play it.In practice, I'd almost always want the 89hh unless the hands are face up. I can play it like the nuts and AA will sometimes fold. If both hands are exposed, then someone should find the cardplayer article, though I can't remember for the life of me who wrote it.

I haven't read it, but I'd like to.I got the idea for this from Bill Chen and Jerrod Ankenmann's book.I'm building to an overall theory point with this.

[Acid_Knight 2]

I haven't read it, but I'd like to.I got the idea for this from Bill Chen and Jerrod Ankenmann's book.I'm building to an overall theory point with this.

I'm pretty sure it's a NL situation that's a little different, but essentially it's a big pair vs a huge draw. I think the hands are face up and the big pair checks in the dark and it goes on to illsutrate what the most EV approach for the big pair is. It was interesting. I really thought it was a Matt Matros article, but I don't see it. I'm trying to think fo whose else write stuff like that.

[NoBBiR 0]

Since the hands are turned over, AA is much easier to play. You have position and can bet when he misses and expect him to call every bet you make, and fold when he hits, knowing you're behind. You also have a redraw if he hits, at least IMO.

[Acid_Knight 2]

Since the hands are turned over, AA is much easier to play. You have position and can bet when he misses and expect him to call every bet you make, and fold when he hits, knowing you're behind. You also have a redraw if he hits, at least IMO.

I don't remember the exact details and I just wasted half an hour looking for the article.It was actually very interesting becuase there's a sequence that makes the play with AA much more +EV than the slight edge that you'd get if you just shove on the flop.Task to everyone: Find the article.

[CobaltBlue 662]

Task to everyone: Find the article.

I believe it was in the issue prior to this most recent one. I'll check when I get home.The more that I think about it...the fact that this is PL instead of NL may really change the answer. This may sound bizarre, but with stack sizes and PL, it might be correct for SB to check/fold to a pot-size bet on this flop. He'd be getting improper odds to continue for just one card...which is essentially what this game is when the hands are face-up.

[tskillz187 0]

I believe it was in the issue prior to this most recent one. I'll check when I get home.The more that I think about it...the fact that this is PL instead of NL may really change the answer. This may sound bizarre, but with stack sizes and PL, it might be correct for SB to check/fold to a pot-size bet on this flop. He'd be getting improper odds to continue for just one card...which is essentially what this game is when the hands are face-up.

I like.

[Acid_Knight 2]

I believe it was in the issue prior to this most recent one. I'll check when I get home.The more that I think about it...the fact that this is PL instead of NL may really change the answer. This may sound bizarre, but with stack sizes and PL, it might be correct for SB to check/fold to a pot-size bet on this flop. He'd be getting improper odds to continue for just one card...which is essentially what this game is when the hands are face-up.

The article that I'm thinking of was from much longer back than that.And yes, PL does make it much different.

[simo_8ball 0]

The more that I think about it...the fact that this is PL instead of NL may really change the answer. This may sound bizarre, but with stack sizes and PL, it might be correct for SB to check/fold to a pot-size bet on this flop. He'd be getting improper odds to continue for just one card...which is essentially what this game is when the hands are face-up.

That's correct, odd as it does sound. In this case, the favourite should check/fold on the flop.We aren't playing a 2 street game here. We are playing two isolated one street games, with the draw having 14/45 outs and no implied odds. If he bets out on the flop, AA should raise because he is >2/1 favourite. Simple as that. If he checks, BB should bet pot, and create just the wrong odds for the draw to continue.The only complicating factor (that I mentioned above) is that while an 8 or a 9 aren't outs, they would easily price the draw in for a pot bet on the turn. While the c/c on the flop is a slight mistake, there *may* be enough value gained on those 6/31 'blank' turn cards to justify calling the flop. I'd have to work it out and I'm not really bothered about doing that.The basic idea is that without any implied odds, a huge draw is simply a 2/1 dog twice.

Pot Limit Holdem Ring gameBlinds: $25/$502 playersStack sizes:Button: $450BB: $450Pre-flop: (5 players) Dealt to BB A A Dealt to Button 8 9 :heart:Button calls dark, BB checks dark. The cards are then turned face up.Flop: J T 2 ($100, 2 players)Now what should the action be in the following 2 cases? The draw is acting first now, and they have $400 each left (a pot bet and pot raise).

This one is FAR more interesting and relevant to the overall picture of draw theory. To make it simpler (and to strengthen the draw's edge), we will assume the draw is a 2/1 dog on both streets (so will win 1 - 0.66*0.66 = 55.5% of the time by the river)Suppose no money goes in at all. Button gets 55.5% of the $100 pot for $455.5 total.Suppose all the money goes in. Button gets 55.5% of the $900 pot for $500 total.This is obvious. He has an edge, so the bigger the pot the more money he makes. So should the draw be happy to get any amount in on the two streets?Suppose the aces check/call a pot sized bet from the draw on the flop and then either the rest of the money goes in on a blank turn or the AA folds to a non-blank:The draw wins $300 pot on the turn 1/3 of the time ($100 net), and wins a $900 pot on the river 1/3 of the time ($300 net). He is getting exact pot odds on both streets, so comes out with exactly the amount he started with on the flop.By getting one pot sized bet in on each street, the draw averages a result of $400. $100 less than if he got allin on the flop. This is the worst he can possibly do (because he always has pot odds he will never have worse than his stack on the flop).The draw makes money by getting either as little money as possible, or as much money as possible in on the flop. By contrast, the Aces do make the most money by charging the draw a proper amount on all streets.So, what should the flop action be? If the aces bet the flop, the draw can shove making the most, so AA should check. When the aces check, if the draw bets out the aces will flat call, which loses the most for the draw.Thus, the flop should (counter-intuitively) actually go check-check. On the turn, the aces will check/fold when the draw hits, or bet a blank now they are a 2/1 favourite and the draw will call.To go back to the initial example, the aces should be happy to get a enough in on the flop such that there is a full pot sized bet left for a blank turn.Summary:When you have a draw you either want to play a big, allin pot (because you know you have good showdown equity and you have some fold equity), or you should try to play a small pot, draw cheaply, and take advantage of good pot odds.On the other hand, if you read your opponent to a draw and you have a made hand, you often want to save a large bet for the turn to extract maximum value when it misses.