shortstack theory

[calc]

when playing the shortstack, I think an important consideration is when to quit the game.

Lets say you play an ultra tight shortstack strategy as described by Ed Miller in GSIH in any no limit game up to 2/5 online or live. You have 20BB.

For the sake of argument lets assume on average you lose 15% of your big blinds in between every double up, slightly more as you build your stack as you will start to play more hands.

Lets also assume on average you are putting you money in as 60% favourite and you are always against an opponent who has you covered.

So lets say you start with 20BB, you go to 17, then double up to 34, then drop back to 28 then double up to 56, then drop back to 45, then double up to 90. So in this instance you were lucky enough to win every time you were all in, and turn your 20BB into 90BB and walk away.

but lets see what happens when you lose that 40% of the time at different stages of your session...

for the sake of this argument I'm assuming you play for the same period of time in each scenario and therefore there will be 3 double up opportunities as an average favourite of 60%. and whenever you go bust you buy back in for 20BB.

There are 8 possible outcomes and the probabilities for each and the net profit/loss for the session is shown.

WWW 21.6% 70BB
WWL 14.4 -20
WLW 14.4 6
WLL 9.6 -60
LWW 14.4 16
LWL 9.6 -60
LLW 9.6 -26
LLL 6.4 -80

Thats a negative expectation where on average we are getting all in as 60% favourite.

I believe the reason for this is that we are disadvantaged when our good luck comes early and our bad luck comes late. As this happens just as often as the reverse, however the effects are more damaging when the bad luck comes last.

any thoughts on this?

[marv]

[ QUOTE ]
when playing the shortstack, I think an important consideration is when to quit the game.

Lets say you play an ultra tight shortstack strategy as described by Ed Miller in GSIH in any no limit game up to 2/5 online or live. You have 20BB.

For the sake of argument lets assume on average you lose 15% of your big blinds in between every double up, slightly more as you build your stack as you will start to play more hands.

Lets also assume on average you are putting you money in as 60% favourite and you are always against an opponent who has you covered.

So lets say you start with 20BB, you go to 17, then double up to 34, then drop back to 28 then double up to 56, then drop back to 45, then double up to 90. So in this instance you were lucky enough to win every time you were all in, and turn your 20BB into 90BB and walk away.

but lets see what happens when you lose that 40% of the time at different stages of your session...

for the sake of this argument I'm assuming you play for the same period of time in each scenario and therefore there will be 3 double up opportunities as an average favourite of 60%. and whenever you go bust you buy back in for 20BB.

There are 8 possible outcomes and the probabilities for each and the net profit/loss for the session is shown.

WWW 21.6% 70BB
WWL 14.4 -20
WLW 14.4 6
WLL 9.6 -60
LWW 14.4 16
LWL 9.6 -60
LLW 9.6 -26
LLL 6.4 -80

Thats a negative expectation where on average we are getting all in as 60% favourite.

I believe the reason for this is that we are disadvantaged when our good luck comes early and our bad luck comes late. As this happens just as often as the reverse, however the effects are more damaging when the bad luck comes last.

any thoughts on this?

[/ QUOTE ]

Provided you are only going to lose on average 15% of your stack between now and the next all-in, and have a 60% chance of doubling up at that point then your EV up to the point immediately after the next all-in is 102% of your current stack (100-15 + 0.6*85 - 0.4*85). This is the only figure you need to worry about.

Some W-L sequences are worse for you than others, but you have no control over them. Walking away will always reduce your EV unless your stack is now so large/small that the 15%/60% assumption breaks down, and as a result your EV-untill-after-the-next-all-in falls negative. Then you leave.

Marv

[slcseas]

Where is your fold equity? I think your analysis is slightly flawed becuase it implies your only means of profit is winning a showdown. With a stack as small as 20 BB you are either pushing pre-flop or raising pre-flop and pushing post-flop. You are removing positional advantage and cutting implied odds to an even money proposition against drawing hands, so you should expect to gain a substantial amount of fold equity.

Using your same variables, look at it from this standpoint.

20BB and ultra-tight pre-flop selection (1 of 10 hands played on average). Online ring game/50 hands per hour, so you are playing 5 total hands in this example. Your cost per round(CPR)1.5BB, is deducted prior to each hand. Assume players are correctly applying gap concept.

Hand #1 - 20 BB. A LAG player who frequently steals opens for 4xBB from the cutoff. It's folded to you in the big blind. You re-pop all-in with K-10. He folds for a profit of 4.5BB

Hand #2 - 23BB after CPR. You open from 3rd positon for 3xBB with AQ. It's folded around the BB who completes. Flop brings 3 low and you take it down with a continuation bet. Minus rake, net profit 3BB.

Hand #3 - 24.5 BB. You raise 4xBB in LMP with 66. You are called by the button, a TAG player who you suspect has 2 overcards. Flop comes A Q 6. You check and he pots, you raise all-in and he folds top pair. 13BB Net Profit.

Hand #4 - 36 BB. Your image is extremely tight so you decide to bluff. You raise 4xBB with 8-7 from EP and get re-raised to 10xBB by the small blind. You fold. Net loss 4BB.

Hand #5 - 31 BB. Player UTG raises 3xBB. You pick up KK and re-pop 9xBB. He pushes and you call. He shows AK, your hand holds up. Approx 60BB after rake.

Your image allowed you to skate with only showing down one hand. In this scenario you only doubled up once and have nearly the same stack as the WWW scenario you described. You simply used your tight image and reads to produce folds. It allowed you to maintain and slowly build your stack, until you could pick the most profitable situation to attempt to double up. By focusing on these low risk-small profit situations, you allow yourself to pick a spot where you can risk your whole stack as a potentially larger favorite than 60/40, and to only do it once.

[WhiteWolf]

[ QUOTE ]

WWW 21.6% 70BB
WWL 14.4 -20
WLW 14.4 6
WLL 9.6 -60
LWW 14.4 16
LWL 9.6 -60
LLW 9.6 -26
LLL 6.4 -80


[/ QUOTE ]

I think your EV numbers are way off in some cases. My numbers using your assumptions:

WLW should be -6 (You double to 34, bust + rebuy, then double to 34 on an initial stake of 40).
WLL should be -40 (you lose 2 buyins, not 3)
LWL should also be -40 (same reason).
LLL should be -60 (lose 3 buyins, not 4)

Using these revised numbers, I still get a EV of -.336 BB per session, still negative but very close to 0. Obviously
you can move this into positive territory by slightly adjusting your initial assumptions. For example, why do you assume that you will always lose 15% of your stack before you hit a double up situation? Your aggression with good hands will pick up some pots uncontested when no one else has a good hand, or when everyone else misses the flop. It could be that you are actually slightly up on average when you are faced with an all-in situation....

[calc]

all in reraise with K10 from the binds?

sure, this is something you might try if the situation was right but it is not short stack strategy. Have you guys read the book? Bluffing and FE preflop is not a big part of the Miller short stack strategy.

Of course there are heaps of variables but what I'm focusing on is the theory that if you fold all but your premium hands then bet strongly preflop and on the flop when you have the advantage you should show a profit. While that is true in a hand by hand analysis my hypothetical shows that even when you can get the bulk of your money in as favourite you still walk away a loser. Which bothers me.

[binions]

[ QUOTE ]
Where is your fold equity? I think your analysis is slightly flawed becuase it implies your only means of profit is winning a showdown. With a stack as small as 20 BB you are either pushing pre-flop or raising pre-flop and pushing post-flop. You are removing positional advantage and cutting implied odds to an even money proposition against drawing hands, so you should expect to gain a substantial amount of fold equity.


[/ QUOTE ]

+1

You win plenty of pots with a pre-flop raise. You win the majority of pots post-flop with c-bet. You fold sometimes on the flop. It's actually unusual to go to showdown. I'd say maybe 15% of the hands you raise pre-flop go to showdown.

[slcseas]

To answer your question, no I have not read the Miller short stack strategy.

But I feel like you are correct in your assessment that you are walking away a loser playing in the way you described. In a short stack situation you simply don't have the luxury of waiting for premium hands. If you do your stack continues to dwindle to a point that when you double up you are just getting back to square one. We seem to agree on a common point, this particular strategy sucks.

As I said previously, your advantages to being short stacked are
A)Not offering enough implied odds to your opponents to allow them to draw correctly. It's an even money prop against a single opponent, and their draws will most often require greater odds to be played correctly.
B)Pushing your stack negates positional advantage.

You need to use these factors to increase your fold equity to produce a +EV. In addition, you need to play enough hands that you can get action on your premium hands. Simply playing your cards only works at the lowest levels of poker. The heaps of variables you describe is what I call "real poker". Each individual hand needs to be played based on the given situation.

Pushing K 10 from the blinds for example, is a play you can expect a positive result on in the situation I described. If you are a theory nut, gap concept says the player in the CO is correct to raise here with a very wide range of cards. His hand strength increases by default because he has only 3 opponents. Also, he will have positional advantage post flop. Lastly, he will win enough uncontested bets from the blinds to make the a positive expectation. From your position in the blind, you are aware of all of these facts. K 10 is a solid starting hand 4 way. Since you give up position and understand a LAG player has a very wide range here, you are playing correctly by pushing your money in with a hand that is likely best right now.

[binions]

[ QUOTE ]
To answer your question, no I have not read the Miller short stack strategy.

But I feel like you are correct in your assessment that you are walking away a loser playing in the way you described. In a short stack situation you simply don't have the luxury of waiting for premium hands. If you do your stack continues to dwindle to a point that when you double up you are just getting back to square one. We seem to agree on a common point, this particular strategy sucks.



[/ QUOTE ]

Ummm, not really. Miller has you playing 46 hands (AA-TT + AK) in early position and in raised pots. That's 3%. In mid position you add 99 + AQ for 68 total hands or 5%. In late position (and SB), you add KQ, AJ, AT and 88-77 for 128 hands or 9%. Bottom line, you see a playable hand every 2-3 orbits on average. While you can get ground down, it doesn't happen as often as you might think.

PS Playing looser with a small stack is a tourney concept.

[calc]

yeah a short stack not only means no implied odds for your opponents it means no implied odds for you, so since your money is going to be all in on the flop or you're folding you should restrict yourself to playing hands that have a high chance of being the best early in the hand.

It will not take you long to become unstuck trying to make moves with a shortstack and bad odds. src in your K10 example even though there is a reasonable chance you have the best hand right now you are giving yourself very bad odds with this play risking 20BB to steal 4. And you could get a very loose call here and still be behind...

the blinds do not increase every 20 minutes in a cash game there is no rush to get your money in there especially if its a shortstack.

and no I don't think the strategy sux I been making money with it fairly consistently for a couple of weeks now I am just running various hypotheticals to see if I can get a better result by adjusting my approach...

[WhiteWolf]

[ QUOTE ]


Of course there are heaps of variables but what I'm focusing on is the theory that if you fold all but your premium hands then bet strongly preflop and on the flop when you have the advantage you should show a profit. While that is true in a hand by hand analysis my hypothetical shows that even when you can get the bulk of your money in as favourite you still walk away a loser. Which bothers me.

[/ QUOTE ]

Like I stated before, your math is off. I've gone back over your numbers and found even more errors.

To restate the assumptions of your model, you start with 20 BB. Every time you buy in or double up, you will chip off 15% of your stack before you are all-in as a 60/40 favorite. You do this until you are all-in three times, regardless of the results.

You then calculate that your first double up gives you a stack of 34. This is correct. You then state that your next double up gives you a stack of 56. This is incorrect. Your stack should be (34 * .85 * 2), or 57.8. You finally state that doubling up 3 times gives you a stack of 90. Once again, this is incorrect. The actual value should be 98.26. Since your model starts out with a very marginal EV situation (see below), underestimating these values has a big impact on your final conclusion.

Rerunning all of the values (result/prob/Net EV):

WWW 21.6% 78.26
WWL 14.4 -20
WLW 14.4 -6
WLL 9.6 -40
LWW 14.4 17.8
LWL 9.6 -40
LLW 9.6 -26
LLL 6.4 -60

I now calculate a +EV of 1.71 BB every cycle of 3 all-ins. In retrospect, a positve result should have been expected from the start. You can't string together a series of +EV bets and get a -EV situation.

(As an aside, please note that your initial assumptions give you a very marginal EV situation, even for a single all-in. A 60% chance of doubling up to 34 (net 14) with a 40% chance of losing 20 gives an EV of (.6 * 14) + (.4 * -20), or just 0.4 BB.)