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Poker questions

Friday, June 09 2006 09:30 PM EDT

Contributed by: jr4284

Math ?

So where's the actual line for justifying that a "push when folded to" strategy is +EV? I'm going to do some math out here, but please, you wizards of probability, correct me if I'm wrong... (Long)

For the sake of simplification, we'll assume that everyone to act after you has an equal "calling range" of any pocket pair, AT+ (suited or off), KQo/s, KJs. I think that's a "fair" range to call a short stack, if a little on the loose side. We will also assume that if one person calls, no one else will.

Pokerstove tells us these things: 12.2% of the time an opponent will be dealt a hand in this range.

Also:
equity (%) win (%) tie (%)
Hand 1: 33.8302 % 33.07% 00.76% { random }
Hand 2: 66.1698 % 65.41% 00.76% { 22+, ATs+, KJs+, ATo+, KQo }

Let S represent your stack in terms of Harrington's M.

Equities:
+(1M) <--Everyone folds
+(S+1M)*.34 =+.34S + .34M <--Call/win
-(S)*.66 = -.66S <--Call/lose
Total "called" equity: -.32S + .34M

Players left to act:

9: (UTG)
(1-0.122)^9=0.310 <-- How often you'll steal the blinds/antes
(+1M)(.31)+(-.32S+.34M)(.69)= -0.221S + 0.5446M
***S = 0.545M/.221 = 2.46M***

8:
(1-0.122)^8=0.353
(+1M)(.353)+(-.32S+.34M)(.647)= -.207S + .573M
***S = 0.573M/.207 = 2.77M***

7:
(1-0.122)^7=0.402
(+1M)(.402)+(-.32S+.34M)(.598)= -.191S + .605M
***S = 0.605M/.191 = 3.17M***

6:
(1-0.122)^6=0.458
(+1M)(.458)+(-.32S+.34M)(.542)= -.173S + .642M
***S = 0.642M/.173 = 3.71M***

5:
(1-0.122)^5=0.522
(+1M)(.522)+(-.32S+.34M)(.478)= -.153S + .685M
***S = 0.685M/.153 = 4.48M***

4:
(1-0.122)^4=0.594
(+1M)(.594)+(-.32S+.34M)(.406)= -.130S + .732M
***S = 0.732M/.130 = 5.63M***

3: (Cutoff)
(1-0.122)^3=0.677
(+1M)(.677)+(-.32S+.34M)(.323)= -.103S + .787M
***S = 0.787M/.103 = 7.64M***

2: (Button)
(1-0.122)^2=0.771
(+1M)(.771)+(-.32S+.34M)(.229)= -.073S + .849M
***S = 0.849M/.073 = 11.63M***

Wow... Definately not what I thought they would be. These numbers shout to me that I'm passing up far too many +EV situations in later positions by folding marginal hands. I never would have thought that you can be sitting with 11M and have an "any 2" push be +EV. Time to loosen up my late position game.

Comments/corrections?

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	Math ?
	Authored by: slart on Friday, June 09 2006 @ 10:54 PM EDT
	Interesting work...a few thoughts though... One thing I see is that your hand isn't random after you've already seen it; some holdings will figure worse against that range than an actual random hand does. So, you should use the equity for your actual holding when you do the calculation. Jamming with any two is only correct if the price is right for EVERY two. I also think your calling range is probably a little misleading. A smaller stack is much more likely to be called than a larger one, for one thing. Also, I think there are too many small pairs in the range, which makes it friendlier to random hands than it probably actually is. [ Reply to This ]

	Math ?
	Authored by: tejasak on Friday, June 09 2006 @ 11:46 PM EDT
	I agree with Slart.. OK math like that really makes my head hurt.. So I go with instinct, and my instinct says Slart dreams about math.. --- Authored by: marco Did he take the free re-buy? [ Reply to This ]

	Math ?
	Authored by: jr4284 on Saturday, June 10 2006 @ 01:14 AM EDT
	I thought about that as I was getting drunk tonight... and found the even prettier beauty of this math work. Reasoning why: it's a +EV play if that is the MAXIMUM you're risking. What happens if the SB is at M=8 and BB is at M=10? An all-in move is STILL a profitable play with any two random cards, because you're dealing with an M=10 or 8 gamble, not M=20, or wherever you actually are. Without a doubt I'm going to apply this to some upcoming MTTs. Naturally, I won't push all in on the button EVERY time it's folded to me, but if I'm at M <12 when it's to me, those chips are going in. Let's see how this unfolds. I'll keep you posted and, with any luck, it will be with "Rail Call" messages. I think the best way to win a tournament is to be the large stack from beginning to end. As impossible as that may be, I'm going to make it my goal. --- Some form of jr4284 or jr4284SAE everywhere. [ Reply to This ]

	Math ?
	Authored by: tejasak on Saturday, June 10 2006 @ 02:11 AM EDT
	I agree, being the big stack start to finish is good.. Now thats math I understand.. With that said, Ive never had that happen in a big MTT.. I like to keep an average stack into the money, then work it.. --- Authored by: marco Did he take the free re-buy? [ Reply to This ]

	Math ?
	Authored by: Batman on Saturday, June 10 2006 @ 02:43 AM EDT
	Ok, to review, as I haven't actually read Harrington's book where he talks about M, it equals the number of chips you need to complete one orbit based on the blinds and antes, from what I surmise. Ok, I get that. At the same time, I think playing by instinct is still the way to go, as nobody said there'd be any math :) Remember, 70% of all statistics are made up :) [J♠] --- Writer, http://www.pokerallstar.com/index.html Owner, http://www.GothamCityPoker.net [ Reply to This ]

	Math ?
	Authored by: kingoftheice on Saturday, June 10 2006 @ 02:55 AM EDT
	The large stack thing works well for people like Ivey. The trick is acquiring that stack. In large online MTT's, the best way to accomplish this is through tight, solid, no bluff play for the first hour or so. Look at the idiots that will call an AI with any ace as a prime example. --- [K♦]oftheice "Hooray for anything at all." -Vin Scully, commenting on two kids jumping up and down in the stands. [ Reply to This ]

	Math ?
	Authored by: marco on Saturday, June 10 2006 @ 09:28 AM EDT
	I went through a similar exercise about 6 months ago using Harrington's Structured Hand Analysis. I was also amazed at how tight I was playing. Pretty much any 2 has a positive EV from late position. Especially against tight opponents. I don't get carried away, but a few moves per tourney can buy you some valuable time. Premium hands just won't come around often enough. SoxFan had a great post a few months back that got a lot of responses. I think it was just before the bubble of the BoDog 100K. Tight player opened with a standard raise and he came over the top for around 20 BB's with A,5 or something like that. Either out of the tourney or add about 30% to his stack. All the aggressive players on here liked the move figuring the villain is only calling with AA or KK. All the tight players were in awe. In the end we pretty much came to the conclusion it was a neutral to slightly positive EV move based on the villain's range. It opened a lot of eyes and got most of the tight players thinking everything thru before just autofolding preflop. --- Rouletteplyr on PP and Paradise [ Reply to This ]

	Math ?
	Authored by: kingoftheice on Saturday, June 10 2006 @ 10:43 AM EDT
	Look at the play that Harrington made in the 2005 WSOP final table with 62 offsuit. Arieh (loose, agressive player) opens for a raise with something like K9 suited. Raymer (also a loose agressive player, though not as loose as Arieh) calls with a weak ace if I remember correctly... and Dan pushes all-in on a stone bluff and gets folded a nice juicy pot; nearly doubled up without anyone seeing his cards. You think he hasn't worked this exercise out before? --- [K♦]oftheice "Hooray for anything at all." -Vin Scully, commenting on two kids jumping up and down in the stands. [ Reply to This ]

	Math ?
	Authored by: Big Blind on Saturday, June 10 2006 @ 12:14 PM EDT
	I think he talked about this one in Vol 2 as an example of the 'Sandwich Play', if memory serves. --- "twodimes, shmoodimes........karma baby" [ Reply to This ]

	Math ?
	Authored by: duquedelsol on Saturday, June 10 2006 @ 03:28 PM EDT
	First of all - I do want to say I think this is a great analysis and potentially a good learning tool...so I dont want my comment's to be seen as negative - simply working on a good project... And - I am far too mentally tired to read all of this and see if this has been discussed - but I think some accomodation has to be made for position in the callers' range... There is no way I am calling an UTG push with AJ/KQ/TT or lower if it is a major part of my stack unless I know the guy is pushing all the time... Similarly - I may call a SB push with A6+/KT+/QJs/44+... Everything is not equal... --- David G Now it's time for the 100 meter dash for people afraid of yellow tape... [ Reply to This ]

	Math ?
	Authored by: BOY de WATER on Saturday, June 10 2006 @ 05:28 PM EDT
	CARD DON'T KNOW MATH.................!!!!!!!!!!! MATH IN NLH JUST GIVE THE LOSER AN EXCUSE AS TO WHY HE SHOULD OF WON..................PLAY THE PLAYER NOT THE CARDS. --- The secret to creativity is knowing how to hide your sources." -- Albert Einstein [ Reply to This ]

	Math ?
	Authored by: jacksup on Sunday, June 11 2006 @ 01:37 AM EDT
	That is nice work, indeed. One thing that jumps out at me is the enormous difference between the cutoff and the button. Another thing to consider, in addition to the fine points slart made, is that just because a play is +EV doesn't make it the best play. For example, you have an M of 11 on the button. So let's say the blinds are 100-200 with a 25 ante and you have 6,050 in your stack. Your work shows that it's slightly profitable to move-in with JTo if the blinds call with the ranges you suggest. But it might be even more profitable to open for 700? I certainly think so. However, for such a big overbet, the range of hands that calls you is probably far tighter, and probably only consists of TT+ and AK. This makes the EV of moving in with JTo = .93(550) + .07(.253(12,500)-6,050)=512-202=310 That's actually a pretty good chunk of change. Hmm, I've never considered open-raising all-in for thirty times the blind, but maybe I should start... Matt [ Reply to This ]

	Math ?
	Authored by: BreakRibs on Sunday, June 11 2006 @ 03:43 AM EDT
	Hey Matt, Poker can be tough! decisions decisions. Is shoving really +ev? Or is there a better play? Fold and survive! or can a player make more by playing the hand after the flop instead of shoving in preflop? > consists of TT+ and AK. This makes the EV of moving in with JTo = .93(550) + .07(.253(12,500)-6,050)=512-202=310 This is definitely interesting... I looked at your #'s and was wondering if perhaps the push with JT returns more, given the blinds only call with TT+, or AK. About 7% of the time one of those hands will be there, and I'm guessing you're saying your JT will win about 25.3% of those hands? well then it only loses 74.7% which means (if I'm right... but I feel crazy questioning your math): EV of moving in with JTo = .93(550) + .07(.253(12,500)-.747(6,050))=512-95 = 417 Maybe the blinds should call with more hands to play optimally, but that would take some guts! Not to mention the fact that you never know if the button is really shoving hands like JT with a stack of 30x the BB! Maybe he's just a tight guy and he has a big hand. -Jim Poker is all LUCK!!! [ Reply to This ]

	Math ?
	Authored by: BreakRibs on Sunday, June 11 2006 @ 05:29 AM EDT
	Oops, I apologize! My math is wrong, and Matt's is obviously correct. I forgot we're looking at the net difference in chips. So yes, it's only worth ~300 as Matt said. Sorry for questioning the math without a clear head. -Jim Poker is STILL a lot of LUCK! [ Reply to This ]

	Math ?
	Authored by: dabluebery on Sunday, June 11 2006 @ 09:58 AM EDT
	What you've stumbled on is an interesting tangent of what David Sklansky just came up with in his new book, "No Limit Holdem, Theory and Practice" The "Sklansky-Chubukov" ranking for each hand assumes a HU pot and $1 / $2 blinds, where you are the SB and the BB can see your cards before you act. The ranking itself, expressed in dollars, tells you how big your stack has to be for each 2-card hand before moving in is incorrect, because your opponent will play perfectly and only call when correct to do so. For pocket kings, you can move in with anything less than like $950 or so. Anything larger and you're going to lose more money to pocket aces than you can pick up in the blinds 99% of the time. For pocket 3's, the number is far lower, like $48 if I remember correctly. There's one illustration he does, with K8o on the button with a 1300 behind and 100/200 blinds. He says that moving in would be profitable even if your two opponents could see your cards, and in reality will definitely be profitable because people will fold many hands they shouldn't (like K-9) when you push all-in for 6.5 times the big blind. Check out that section, it's good stuff. It almost seems like a continutation of the "Game Theory" chapter from Matt's book. --- "Its not a joke when its directed at you." [ Reply to This ]

	Math ?
	Authored by: jr4284 on Sunday, June 11 2006 @ 06:19 PM EDT
	First, I'm glad that this post has generated a good discussion. Second, as slart mentioned in the first reply, once you see your cards, they're not longer "random," and therefore the equities aren't as listed in my calculations. It got me curious as to what the neutral EV line would be for specific hands, but working each hand out position by position is a pain in the ass, so I created a spreadsheet to do it for me. I'm sharing it here: http://www.savefile.com/files.php?fid=6267761 I listed off some basic equity values for a few hands that I thought would give a good "feel" for groups of hands. Of course, 2 seconds with PokerStove and you can grab the exact equity for any two cards. I'm finding out many little bits of information playing around with this spreadsheet. I've only played 2 MTTs since working these numbers, and both ended quickly with JJ into QQ and QQ into KK, so hopefully a larger sample will provide me with a good feel for how this theory applies to practice. dbb: Thanks for mentioning another book that I'm going to have to read now =) --- Some form of jr4284 or jr4284SAE everywhere. [ Reply to This ]

	Math ?
	Authored by: Grasshopp3r on Sunday, June 11 2006 @ 11:01 PM EDT
	Kill Phill by Blair Rodman takes the push ideas to the extreme. What I have found is that the better the opponents, the more willing they are to lay it down. You also get moved a lot in a large MTT, so the opponents do not get wise to the strategy. --- Grasshopp3r on FTP, PS and Bodog Grashp3r on Pacific Poker & Sun Poker I will lighten up. [ Reply to This ]

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