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Old 09-19-2007, 10:48 PM   #1
Cry Me A River
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Pooh-Bah - Crushing Short Stacks

I should hit 5K posts sometime in the next couple weeks. Consider this an early Pooh-Bah post.

Like the weather, everyone talks about short stackers but nobody does anything about them. This is the thread where you learn not only how to deal with them, but how to crush them.

There are a couple things you need to keep in mind. Dealing with short stacks is higher variance than dealing with big stacks. What would normally be small pots become medium sized pots. Short stacks generally only play, at most, 2 streets. These two factors mean you tactics against short stacks may be radically different from your tactics against full stacks. If you do not have the bankroll or the stomach to deal with this you need to find another game. All the whining in the world is not going to change a structure that is VERY profitable to the poker sites.

Your only recourse is to learn to beat the short stacks.

If you take nothing else away from this post, think of this. Short stacks are successful because they have no difficult decisions on later streets, they rely on fold equity and abuse full stacks who are loathe to take a coin-flip or get it in as a dog even when pot odds dictate they should.

The thing is, there is no reason you can't do this too.

When you are head's up against a 20BB short stack, you ALSO have a 20BB stack. So all those moves you hate? Pushing over your preflop raise? Donk-pushing flop?

Well you can do those too.

And they're just as devastating when used against a short stack as when used by one. Even more so because short stacks don't ever get to win 100BB pots to make up for those losses. The only real advantage a short stack has over a full stack is the ability to squeeze two full stacks against each other and force full stacks to fold for fear of other full stacks. However this advantage is often only one of perception. In such a squeeze, the other full stack is likely to be as afraid of you as you are of him. So you should usually concentrate on the short stack.

So even though you may not have odds to call against a short stacker's raise, call him anyway and then open push flop with ATC and see what happens. Do this sometimes with big pairs too to put the fear if god in him.

Any chip you take from a short stack hurts him worse than the chip he takes from you. Any time you get him to fold after he's put a third of his stack in it's a smack in the mouth. And any time you stack him it's a knife in the gut.


The way to beat any enemy is to analyze their strengths and weaknesses, then avoid or neutralize those strengths and exploit their weaknesses.

Advantages to Short stacking
Fold equity and Gap concept
Only have to play preflop and flop, no worries about what to do against scare cards etc on later streets
Opponents seldom have odds to chase draws
Full stacks who hate shorties and play badly against them


Disadvantages/mistakes from short stacking
No implied odds
Low ceiling to the amount won with monsters
Need to push with a wide range to be profitable
Short stacking is a limited game plan with no depth that tends to rely on mathematics and tight opponents who fold too much
High variance


From this I have derived three keys to victory against short stacks. They are:

1) Know your shorties. Not all short stacks play the same.
2) Effective stacks and pot odds. Know when you have to get it in with the worst of it.
3) Raise, raise, raise. To exploit shorties, the price of playing poker MUST go up.


Know your shorties
Obviously everything is on a continuum, there are seldom absolutes. However, I am going to group short stackers into three basic types.

The Good Short Stackers
Good short stackers are the guys you hate. The ones who have a clue and put you to tough decisions. Fortunately These kinds of short stacks are in the minority. And even so, you can make their life just as difficult by putting THEM to the tough decisions.

Tight, Bad Short Stackers
Tight, bad short stackers are the short stackers with reasonable preflop stats, something like 12/6/2. However, they are still very bad. These are the guys who sit in with 20BB and call preflop raises with 44. These are the guys who don't abuse their fold equity. These guys are generally sitting with short stacks NOT because they know how to play short but because they're either scared money or short rolled.

Loose, Bad Short Stackers
Loose, bad short stackers are the nuts with stats like 40/20/4 who are looking for any excuse to gamble and get their stack in. These guys are basically free money, however, they can be VERY high variance.

These three different types of short stacks require slightly different approaches to play against and exploit.

Spotting the loose/bad short stackers is generally quite easy just from their stats. Differentiating between the good short stackers and the bad tight short stackers can take a little more time.

You can spot the bad tight short stackers because the make bad plays. In particular, they will try to set mine or call raises with suited connectors without anything resembling implied odds and then fold flop.

Essentially, short stacks, particularly short stacks around 20BB should be calling raises almost never. There are a few situations where calling preflop raises with a short stack is a good idea and I'll outline a couple here so you can spot them:

- If the short stack has a big pair QQ/KK/AA and the player raising preflop is likely to fold to a 3bet/push the short stack may be wise to just call a preflop raise and try to get it in on the flop.
- If the preflop raiser is weak-tight and likely to fold flop too much then the short stack can call and push flop with a wide range and make a lot of profit from these bad folds.

If you see a short stack calling raises outside of these parameters then you're likely dealing with a bad short stack, or at least a short stack who is not playing optimally.

It's important to know which type of short stack you are dealing with since it helps determine their hand ranges and how best to implement the other parts of our plan.


Effective stacks and pot odds
This is really the meat of the equation.

If you are having a hard time against short stacks, you are almost certainly folding too much.

There are three very common situations you face all the time against short stacks. They are:

1) You raise preflop, short stack pushes all-in. Everybody else folds. Do you call or fold?
2) Short stack limps, you raise preflop, short stack calls and pushes flop.
3) Short stack limps, you raise preflop, you cbet and short stack checkraises all in; OR You raise preflop, short stack calls, you cbet flop and short stack pushes all in.


Situation 1)

In this situation, the short stack usually has 20BB to 30BB. Larger short stacks don't usually push preflop like this and if they do you should probably treat them like full stacks. So the question is, what do we call with here?

This all depends on the range we can put the short stack on. We need to do that first.

If the short stack is of the loose, bad variety his range is very wide. Something like 88+/AT+ is not unreasonable. Some will do this with any pair, some are pushing KQ or KJ here as well.

However, we will stick to 88+/AT+

The tight, bad short stacker actually has the tightest range here. He isn't good enough to take full advantage of his fold equity and he's waiting for a hand that gives him a good chance to double up. He's not looking to re-steal. So a reasonable range here is JJ+/AQ+.

The good short stacker is the toughest to put on a range. This is because he's good enough to try and abuse his fold equity. So his range here is going to be somewhat dependent on your raising range and position. If you're in a position where your raising range is wide (i.e., button) and/or you're an aggressive raiser his pushing range will be much wider than if you are a nitty player. In addition, he may take into consideration whether or not you fold too much to short stack pushes.

For the purposes of the math that follows, we are going to assign good short stackers a range here of TT+/AJ+. However, keep in mind that their range may be almost as wide as the loose short stacker or as tight as the bad/tight short stacker. You need to adjust your reads according to the situation. I will use these three ranges to give you an idea of where you stand in a variety of scenarios.

Scenario 1A)

Short stack has 20BB and is not in the blind. You raise 4BB. Short Stack pushes. Everyone else folds. The pot is 25.5BB and you need to call 16BB.

You need a hand which has 38.55% equity against short stack's range to make a call break-even.

If short stack has a range of 88+/AT+
AK has 55.54% equity vs range
AQ has 47.26% equity vs range
AJ has 39.186 equity vs range
AT has 31.63% equity vs range
99 has 45.61% equity vs range
88 has 41.83% equity vs range
55 has 39.88% equity vs range
44 has 39.41% equity vs range
33 has 38.87% equity vs range
22 has 38.28% equity vs range
76s has 32.8% equity vs range

If short stack has a range of TT+/AJ+
AK has 54.19% equity vs range
AQ has 42.49% equity vs range
AJ has 31.18% equity vs range
TT has 43.79% equity vs range
99 has 40.86% equity vs range
44 has 39.93% equity vs range
33 has 39.36% equity vs range
22 has 38.75% equity vs range
76s has 33.39% equity vs range

If short stack has a range of JJ+/AQ+
AK has 50.11% equity vs range
AQ has 33.07% equity vs range
JJ has 42.745% equity vs range
TT has 40.11% equity vs range
99 has 39.32% equity vs range
66 has 39.25% equity vs range
55 has 39.044% equity vs range
44 has 38.525% equity vs range
76s has 32.772% equity vs range

As you can see you're going to be getting it in behind the short stack's range quite a bit. However, the dead money in the pot dictates your calling range.

Against the loosest range, call 33+/AJ+.

Against the medium range, call 22+/AQ+.

Against the tightest range, call 55+/AK+.

In addition, this assumes villain has a stack size of exactly 20BB. This often isn't the case. So, how small a stack does villain need to have to make calling with 22/AQ/76s break-even in those situations above where it is otherwise a fold?

If villain has an 18BB stack, the pot is 23.5BB and you need to call 14BB. Break-even is 37.33% equity.

If villain has an 15BB stack, the pot is 20.5BB and you need to call 11BB. Break-even is 34.92% equity.

Villain's stack actually has to get down around 10-11BB for the equity value to shift enough to make 22/AQ/76s calls in these situations.


Scenario 1B)

Short stack has 30BB and is not in the blind. You raise 4BB. Short Stack pushes. Everyone else folds. The pot is 35.5BB and you need to call 26BB.

You need a hand which has 42% equity against short stack's range to make a call break-even.

As you can see pot odds are such that you need a much tighter calling range.

Against the loosest range, call 99+/AQ+.

Against the medium range, call TT+/AQ+.

Against the tightest range, call JJ+/AK+.


Scenario 1C)

Short stack has 20BB and is in the big blind. You raise 4BB. Short Stack pushes. Everyone else folds. The pot is 24.5BB and you need to call 16BB.

You need a hand which has 39.5% equity against short stack's range to make a call break-even.

Against the loosest range, call 55+/AJ+.

Against the medium range, call 44+/AQ+.

Against the tightest range, call 55+/AK+.

So the fact that the short stack is in the big blind does mean your pot odds are not as good and you need to tighten up your calling range a little. But not a lot.


Scenario 1D)

Short stack has 30BB and is in the big blind. You raise 4BB. Short Stack pushes. Everyone else folds. The pot is 34.5BB and you need to call 26BB.

You need a hand which has 42.98% equity against short stack's range to make a call break-even.

As you can see, due to the larger stack size the fact villain is in the blind doesn't make much difference. So at 30BB in or out of the blinds can be ignored unless it affects the short stack's range (i.e,; big blind will have a wider push range against an open raise from the button than a raise UTG)



The thing to take away from this is that calling these pushes is never far wrong. And if there are any mitigating circumstances, particularly other limpers or other players calling your raise, some of the close folds (like AJ or 76s) can quickly become calls. And this is assuming fairly tight pushes, you know sometimes these guys are pushing with 76s themselves.

The point is that you're probably making a mistake by folding too much and NOT by calling too much.



Situation 2)

In this situation, short stack limps, you raise preflop to 5BB, short stack calls and pushes flop.

On the flop, the pot is 11.5BB. Villain pushes 15BB. You need to call 15BB to win a 26.5BB pot.

You need 36.14% equity in this pot to make this call.

Obviously there are hundreds of possible scenarios here, I can't list all of them. But here are some things to keep in mind.

Bad, loose short stacks and good short stacks have a huge pushing range here, though for different reasons. The loose short stack can't wait to get his stack in and gamble. All the better if he can push you off pots. The good short stack has a hand sometimes, but he also wants to exploit his fold equity by making you fold the better hand.

Bad, tight short stacks actually have the tightest range here by far. They are unaware of fold equity. They're check/folding any flops that miss them. If one of these guys pushes they usually have at least TP or a big draw.

So let's examine some standard situations to see how much equity you typically have. I'm going to assume it goes without saying that you are calling the push with TP or better and any good draws.

Overcards vs pocket pair:

Board: 2c 2d 9s
equity win tie pots won pots tied
Hand 0: 24.343% 24.04% 00.30% 238 3.00 { AcKd }
Hand 1: 75.657% 75.35% 00.30% 746 3.00 { 6c6d }


Pocket pair vs bigger pair

Board: 2c 2d 9s
equity win tie pots won pots tied
Hand 0: 08.384% 08.38% 00.00% 83 0.00 { 7c7d }
Hand 1: 91.616% 91.62% 00.00% 907 0.00 { Tc9d }


Middle pair with overcard vs top pair

Board: 2c 9s 5d
equity win tie pots won pots tied
Hand 0: 25.286% 25.29% 00.00% 751 0.00 { Ac5c }
Hand 1: 74.714% 74.71% 00.00% 2219 0.00 { T9s }



These look pretty bleak, but only if the short stack has EXACTLY those hands. Against bad, tight short stacks we can often take them at their word and just fold.

However against loose short stacks and good short stacks their range is usually much wider. So we will try to assign some appropriate flop push ranges:

Loose short stacks will call preflop with a very wide range and push anything that hits their hand or if they think flop did not hit you.

Good short stacks have a much narrower calling range preflop. They know not to try and set mine. However, they may call with a wide range if they think you are likely to fold preflop to their push, particularly if your raising range is wide (i.e.; from the button).

I'm going to eliminate big pairs under the assumption they would have been raised preflop. This may not always be the case, but usually it should be.


Against a loose short stack, pushing range on this flop and our equity in these hands looks something like:


Board: 2c 2d 9s
equity win tie pots won pots tied
Hand 0: 49.146% 43.81% 05.34% 62017 7558.50 { AcKd }
Hand 1: 50.854% 45.52% 05.34% 64436 7558.50 { TT-22, ATs+, KJs+, J9s, T9s, 98s, ATo+, KJo+, J9o, Tc9d, 98o }


Board: 2c 2d 9s
equity win tie pots won pots tied
Hand 0: 58.971% 58.42% 00.55% 95434 895.50 { 7c7d }
Hand 1: 41.029% 40.48% 00.55% 66125 895.50 { TT-22, ATs+, KJs+, J9s, T9s, 98s, ATo+, KJo+, J9o, Tc9d, 98o }


Board: 2c 9s 5d
equity win tie pots won pots tied
Hand 0: 59.909% 59.67% 00.24% 89201 357.50 { Ac5c }
Hand 1: 40.091% 39.85% 00.24% 59574 357.50 { TT-22, ATs+, KJs+, J9s, T9s, 98s, ATo+, KJo+, J9o, Tc9d, 98o }


Against a good short stacker it comes down to figuring out what he's calling raises with. He should be calling raises very rarely unless he thinks he can push-steal against you on the flop. If he's going for a steal, his range is going to be similar to the loose short stacker. If he's not stealing then you can expect him to push TP or better like the bad/tight short stacker and you should be prepared to get out of his way.

You need to try and track what the good short stacker is doing. If he's calling raises with a fairly wide ranges and trying to steal on flops then you need to call him down lightly. If he's playing tight against raises then you have to be prepared to fold marginal hands.


As the short stack's stack gets bigger, you need better equity to call his flop push.

If short stack starts with 30BB On the flop, the pot is 11.5BB. Villain pushes 25BB. You need to call 25BB to win a 36.5BB pot.

You need 40.65% equity to call.

If short stack starts with 40BB On the flop, the pot is 11.5BB. Villain pushes 35BB. You need to call 35BB to win a 46.5BB pot.

You need 42.94% equity to call.

So while you should be tightening up your calling range slightly, keep in mind that you after still have plenty of equity against the short stack's range.

The other big thing to keep in mind on flops is turning the tables on the short stacker.... Call his preflop raise and then push flop. Or push over his preflop raise. Put HIM to the tough decision for all his chips. This can work just as well against the short stacker as it does for him.



Situation 3)
Short stack limps, you raise preflop, you cbet and short stack checkraises all in; OR You raise preflop, short stack calls, you cbet flop and short stack pushes all in.

This situation almost becomes trivial against a 20BB stack. If the pot on the flop is 9.5BB, say you cbet 7.5BB. Short stack then pushes his last 15BB. You need to call 15BB in a 32BB pot.

You only need 31.92% equity to call which you will have with a very wide range of hands.

Against a 30BB stack, if the pot on the flop is 9.5BB, say you cbet 7.5BB. Short stack then pushes 25BB. You need to call 25BB in a 42BB pot.

You need 37.3% equity to call.

Against a 40BB stack, if the pot on the flop is 9.5BB, say you cbet 7.5BB. Short stack then pushes 35BB. You need to call 35BB in a 52BB pot.

You need 40.23% equity to call.


The last thing to consider here is that even head's up, you don't HAVE to cbet against the short stack. If you KNOW he's going to push over you and you don't have a hand that can call him then don't cbet. Either take the free card or let him bet and then YOU push over him and let him decide if he has enough equity. In fact, you should do this sometimes when you DO have a hand you want to felt. So he can't put you on a hand in these situations and sometimes HE has to fold the best hand.


Finally, when it comes to your preflop raising, keep in mind what, if any short stacks are in the hand (or left to act behind you) and whether they're likely to push on you either preflop or on the flop. If they are, then you may want to consider tightening up your range and not raising hands like 76s. Rather only raise hands that you will be able to get all-in on a wide variety of flops. Or if you do still raise 76s, try to do so in situations where you're likely to have good odds postflop even if the short stack pushes. For example, multi-way with several players calling the raise. In this case, also consider raising a smaller amount that your usual 4BB+1 to juice the pot rather than isolate.


Raise, raise, raise
Short stacks do not want to call raises unless they're planning to push-steal a lot of flops. The worst thing you can do to a short stacker is raise his limps, raise his blinds and 3bet his raises. Remember, he has no or very bad implied odds. And in raised pots he shouldn't have much fold equity against you. This is the worst possible situation for him to be in.

You want to raise a short stack as much as you possibly can. Yes this will lead to high variance situations when he comes over the top, however you usually know when you have the best of it.

For example, if a good short stacker overlimps from late position, you know he almost always does not have much of a hand or he would raise. So you need to raise. This forces him to fold 33 or 76s because he doesn't have odds to call and try to outflop you. Unless he's going to try push-steal flop. But his range is already well defined. So you know that on the flop you're going to have good equity to call his push. And if he realizes you're playing him tough this way he doubly can't afford to call because he no longer has the benefit of fold equity on the flop. So he needs to fold to your raise; calling becomes a big mistake.

If he open raises, 3bet him liberally. His choice here becomes one of folding or pushing. He knows he has little fold equity against you and he can't afford to put in half his stack and fold flop very often. This becomes a very difficult situation for a short stack particularly if you keep 3betting him and raising his limps.

You do not want to let short stacks see too many cheap flops. You also do not want to give them the opportunity to be the aggressor and exploit the gap concept and their fold equity. Raise them. Put them all-in before they put you all in.


Leveling
Keep in mind that several posters here short stack some time or all the time (also lurkers!). If they are aware that you will have read this post they may start adjusting their ranges against you. For example, if they think you've started folding AQ against their preflop pushes, they may start pushing with a MUCH wider ranger to exploit your propensity to fold. On the other hand, if they see you widening your range against them they may tighten up. Against the bad short stackers you really don't have to worry. But watch out for the good ones making adjustments to your game.


Final Words
Good short stackers are difficult to play against. OTOH, bad short stackers of both the loose and tight variety are very transparent and often amount to free money, particularly if you are willing to play them tough. If you can learn to play well against the bad short stackers they will more than make up for the good ones. What's more, the good short stackers are not unbeatable either. You just need to start playing them as short stacks NOT as big stacks who sit out the turn and river.

A lot of it is putting yourself in very marginal positions, but, the short stacks make a lot of profit getting people to fold too much. The only way to combat that is to not fold when you have decent equity, ensuring that they share in these tough spots. This can lead to very good things for you from a meta-standpoint if short stack alters his play so as to avoid you and not try to push you off hands very often. Thus taking away all the advantage that comes from short stacking.
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Old 09-19-2007, 10:50 PM   #2
Das Budrick
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Re: Pooh-Bah - Crushing Short Stacks

this is a fantastic post, thank you very much
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Old 09-19-2007, 10:52 PM   #3
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Re: Pooh-Bah - Crushing Short Stacks

I thought pooh-bah was at like 1600?
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Old 09-19-2007, 10:56 PM   #4
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Re: Pooh-Bah - Crushing Short Stacks

Quote:
I thought pooh-bah was at like 1600?
I like anniversaries. Call me sentimental.
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Old 09-19-2007, 11:07 PM   #5
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Re: Pooh-Bah - Crushing Short Stacks

This is probly the most in depth and informative post ive ever had the pleasure of reading. NH sir and congrats!
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Old 09-19-2007, 11:09 PM   #6
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Re: Pooh-Bah - Crushing Short Stacks

nice post, added to favs cause im too tired to read and get the max out of it right now.
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Old 09-19-2007, 11:16 PM   #7
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Re: Pooh-Bah - Crushing Short Stacks

Looks great. Ill give a complete read when i get a spare hour
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Old 09-19-2007, 11:23 PM   #8
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Re: Pooh-Bah - Crushing Short Stacks

unreal...longest post in history. I look forward to reading it.
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Old 09-19-2007, 11:28 PM   #9
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Re: Pooh-Bah - Crushing Short Stacks

No, this is the longest post in history:

The Collective Wisdom of 2+2

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Old 09-19-2007, 11:34 PM   #10
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Re: Pooh-Bah - Crushing Short Stacks

Thank you for taking the time to do this. You have put into words what my pea brain has been trying to work out for the last few weeks.
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Old 09-19-2007, 11:45 PM   #11
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Re: Pooh-Bah - Crushing Short Stacks

Excellent post, CMAR
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Old 09-19-2007, 11:53 PM   #12
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Re: Pooh-Bah - Crushing Short Stacks

awesome post, like others im gonna save it and come back to it
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Old 09-20-2007, 12:49 AM   #13
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Re: Pooh-Bah - Crushing Short Stacks

Please delete. Also, you have one sentence in there that can make you almost unbeatable in one aspect. Too bad for you that there is no way I divulge it unless I decide to give up shortstacking forever.
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Old 09-20-2007, 01:43 AM   #14
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Re: Pooh-Bah - Crushing Short Stacks

Great post
Your contributions to this forum are amazing CMAR
It is a shame that most of us are too ADD to read carefully through the whole thing or will get too drunk tonight and forget it.
The full extent of your wisdom may be lost in time, like tears in rain
(watched it this weekend)
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Old 09-20-2007, 02:38 AM   #15
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Re: Pooh-Bah - Crushing Short Stacks

Quote:
Please delete.
No.

In any game or competition, whenever a strong but unbalanced strategy arises it is also always it's own Achilles' heel.

There is obviously no way to discourage bad short stackers. They short stack because they don't know any better. What's more, they are generally so exploitable we don't want to discourage them.

Against those players, the tactics I've outlined will not get rid of them, they will only increase your earn against them.

However, against good short stackers my tactics will have two effects.

They will cut their profitability considerably and send their variance through the roof. Good short stackers play that way because they see it as a viable, profitable strategy. And they're the ones who will seek new strategies when it starts to fail.

If a large number of full stacks begin taking this approach, short stacking will begin to fail.

Quote:
Also, you have one sentence in there that can make you almost unbeatable in one aspect.
Only one?

You've given me a good idea though. A cliff-notes version that only lists the tactics and not the reasons why. For people who don't want to read the whole thing and just want a straight-foreward playbook on how to cripple shorties.

Tomorrow...
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Old 09-20-2007, 03:52 AM   #16
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Re: Pooh-Bah - Crushing Short Stacks

No wonder you haven't been posting in the Grey Swan of late. Seriously good effort.
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Old 09-20-2007, 04:40 AM   #17
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Re: Pooh-Bah - Crushing Short Stacks

Nice post, very interesting read
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Old 09-20-2007, 04:53 AM   #18
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Re: Pooh-Bah - Crushing Short Stacks

Outstanding, C!

Definitely one of those that will need to be read more than once, which will perhaps make up for the amount of time and effort you must have put into creating it.

Thank you!!
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Old 09-20-2007, 05:13 AM   #19
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Re: Pooh-Bah - Crushing Short Stacks

CMAR
v. nice, ModOfTheYear vote from me.

CDL - be cool, just play as a good SSer, it remains unexploitable strat.
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Old 09-20-2007, 05:48 AM   #20
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Re: Pooh-Bah - Crushing Short Stacks

OP is better than most Cardplayer and Bluff columns.

Quote:
OP is better than most Cardplayer and Bluff columns
QFT

P.S. CHOO CHOO!!!
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Old 09-20-2007, 07:35 AM   #21
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Re: Pooh-Bah - Crushing Short Stacks

This is a very, very good post. Thanks, CMAR!
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Old 09-20-2007, 07:52 AM   #22
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Re: Pooh-Bah - Crushing Short Stacks

jesus, Im short stacking nl25 and nl50 atm to clear the stars bonus as my roll is a bit short, I will def have to give it up now once I've finished my bonus.
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Old 09-20-2007, 09:45 AM   #23
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Re: Pooh-Bah - Crushing Short Stacks

Looks good. I am about half way through it.
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Old 09-20-2007, 09:51 AM   #24
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Re: Pooh-Bah - Crushing Short Stacks

Wow dude. Great read. This should be submitted to the magazine for an easy $200.

Props.
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Old 09-20-2007, 09:58 AM   #25
threads13
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Re: Pooh-Bah - Crushing Short Stacks

Quote:

You need a hand which has 38.55% equity against short stack's range to make a call break-even.

If short stack has a range of 88+/AT+
AK has 55.54% equity vs range
AQ has 47.26% equity vs range
AJ has 39.186 equity vs range
AT has 31.63% equity vs range
99 has 45.61% equity vs range
88 has 41.83% equity vs range
55 has 39.88% equity vs range
44 has 39.41% equity vs range
33 has 38.87% equity vs range
22 has 38.28% equity vs range
76s has 32.8% equity vs range

If short stack has a range of TT+/AJ+
AK has 54.19% equity vs range
AQ has 42.49% equity vs range
AJ has 31.18% equity vs range
TT has 43.79% equity vs range
99 has 40.86% equity vs range
44 has 39.93% equity vs range
33 has 39.36% equity vs range
22 has 38.75% equity vs range
76s has 33.39% equity vs range

If short stack has a range of JJ+/AQ+
AK has 50.11% equity vs range
AQ has 33.07% equity vs range
JJ has 42.745% equity vs range
TT has 40.11% equity vs range
99 has 39.32% equity vs range
66 has 39.25% equity vs range
55 has 39.044% equity vs range
44 has 38.525% equity vs range
76s has 32.772% equity vs range

As you can see you're going to be getting it in behind the short stack's range quite a bit. However, the dead money in the pot dictates your calling range.

Against the loosest range, call 33+/AJ+.

Against the medium range, call 22+/AQ+.

Against the tightest range, call 55+/AK+.

In addition, this assumes villain has a stack size of exactly 20BB. This often isn't the case. So, how small a stack does villain need to have to make calling with 22/AQ/76s break-even in those situations above where it is otherwise a fold?

If villain has an 18BB stack, the pot is 23.5BB and you need to call 14BB. Break-even is 37.33% equity.

If villain has an 15BB stack, the pot is 20.5BB and you need to call 11BB. Break-even is 34.92% equity.

Villain's stack actually has to get down around 10-11BB for the equity value to shift enough to make 22/AQ/76s calls in these situations.
Our equity is larger with(vs that range) so we should call vs that range with 18BB stacks and 15BB stacks, should we not?

The rest checks out very well. Nice post, I think it was needed with all the people whining about short stacking but not learning to play against it.
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