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Playing the odds with Middle pairs.
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Written by krishna
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Sunday, 07 December 2008 23:46 |
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Page 2 of 4
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Thanks, this is really good stuff.
Hands like 22 - 55 does the same rule still apply or is it more of a fold.
Also how should you play AK if you suspect they have pair? orange m
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I may have picked this up from Harringtons book but if I am orange Mzone im pretty much folding anything under 77 in early position, and if its later then perhaps trying to get in cheap or fold to a raise.
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Yeah, i neeed to get around to reading that book
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Ok, couple of ways to look at this.
Harrington says that Suited Connectors and small pocket pairs are no longer playable from yellow and orange M. The reason he says that is that you do not have the implied odds to chase hitting a set or flush/straight profitable.
IMO whilst that is true, it does not mean that you cannot steal with these hands from yellow or orange M. If you stop playing PPs and SCs al together, you are just not playing enough hands. Remember, from yellow and orange M the correct approach is actually to play MORE hands, not less. (In SNGs - including MTT SNGs there can be some bubble and stack size dynamics which influence this a bit too though).
Anyway, I mentioned at the start there were a couple of ways to look at it...
The second is Ryan Fisler's approach of using orange M as a re-shove zone. With an M of between 12 and 8 you usually have re-shove fold equity. Instead of making a play for the blinds only, now your re-shove is making a play for the blinds plus the open raise, so its normally aiming for 4.5BBs instead of 1.5. Accordingly it needs to work only half as often to be profitable. If called you will be guaranteed for a race or be dominated, but now the reward is also higher being an immediate ticket back to high yellow or green M. So the Fisler approach has loads of merit too. It does take some tones to re-shove with pocket 5s though and profiling comes into whether or not you should do it in specific situations.
The last thing to consider is the chances of being up against a higher pocket pair, which is the disaster scenario.
For this, Phill Gordon's PP rule comes into play.
The rule is C = (N x R) / 2
Where C is the % chance you are facing a higher PP, N is the number of players still to act and R is the number of possible PPs higher in rank than yours.
If you have 33 UTG at a 9 player table, then there are 11 higher PPs, and 8 players left to act. The chances someone has you dominated are therefore 45%. Notice however that lots of these PPs may not be able to call an all in bet on the flop. If you called with 66 and the flop came 9QA would you call all-in on the flop?
However if you wanted to accept a 25% chance that you were dominated, then you can make this play with 88 UTG (there are 6 higher PPs, 8 players to act to making it a 24% chance of domination) Is a 25% chance +ve EV?
75% of the time you will be up against big slick or similar
25% of the time you will be dominated.
Lets start with the 8M 2400 stack with blinds of 100/200
There are 2 events to consider. 1 is you are dominated, 2 is you are facing unpaired high cards.
Event 1. Assume the higher PP will always call your all-in on the flop. This is pretty unrealistic since 99 or TT will often fold to a big fat scary flop, but lets make 100% calls a worse case scenario.
If your 88 is up against something like JJ, you will be playing for 2400 chips and you will lose about 80% of the time. So over 100 hands you win 48000 and lose 192000 making for a deficit of 144K
Event 2 is big slick and AQ type hands
In this event there are two main sub events..
2(a) is AK misses and folds. This will happen 70% of the time, giving you positive 105000 over 100 hands.
2(b) is AK hits on the flop and you also flop a set or later improve to a set. The chances of flopping a set are about 7.5:1 or 12%. The odds of improving to a set after missing the flop are about 8%. Flopping or later improving are equally as good so we can add them together for 20% chance of beating TPTK.
Out of our 30 hands left, 6 of them fit this category, where we win 2700 each time or 16200 over 6 hands.
The remaining 24 hands, we lose to TPTK for 2400 each time or 57600 total loss.
Putting that all together,
In the we are dominated situation we lose 144K in 100 hands, which is 1440 per hand or 7.2BBs .
In the "we are facing big slick" situation, we win 63600 or 636 each hand or 3.18 BBs per hand.
If we stand to lose 7.2BBs in event 1 (being dominated) and win 3.2 in event 2 (facing AK), what is our acceptable risk of being dominated?
The minimum acceptable risk must be break even, so
3.2Y = 7.2 x (100-Y)
where y = acceptable % risk
Y = 31%
Which mean a 25% risk tolerance threshold is somewhat conservative but probably about right given that the less we push marginal situations, the more time you can wait for genuinely good situations.
Accordingly, from Orange M, you can make this play from UTG with 88 plus.
From UTG+1, 77 achieves 24.5% risk of domination
From EMP (6 players left) 66 works
From MP with 5 players left, 44 works
Let me know if anyone disagrees with any of this. I am not suggesting it is gospel, rather I'm working it out as I go
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Interesting discussion, but I have always leaned to shoving it in, because it is rather difficult to play a flop if you get called. What might be missing here is who, not how many are behind you, how close to the money, and what profiles are in the blinds.
I think I have played this situation more intuitively up until now, but this math is def something to ponder David - requires a closer look by me to be sure.
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The benefit of raising and shoving is that it IMO it tends to give you slightly more fold equity on the flop. If you are resigned to be playing for your whole stack anyway, its doesn't really matter how you get it all in, other than if one way creates more fold equity than another, then the higher fold equity approach must be higher (I would think)
Having said that, if AK does fold on the flop, then you have only won 1500 chips whereas if you shoved and won the race to the end, you would win 2700. That 1200 difference may turn out to be significant in terms of how long it will be before you are back in high risk waters...
The next task is to look at what happens from an M of 6 and then less than 5.
I'll also give a little more thought to comparing equity between raise and shove versus open shoving from an M of 8.
Those two tasks will however have to wait till a few more homely duties are attended to Laughing
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OK, M of 8, stack of 2400, blinds of 100/200....
Instead of 1/2 stack raise then shove, how does open shoving compare?
Our 1/2 pot raise was 1200 (6BBs) Are there any hands that can call a 6BB bet but fold to a shove for 12BBs? Probably not. So we are still getting called by bigger PPs and AK / AQ type hands and still getting called at the same frequency
Against the bigger PPs nothing changes. We still lose 144K in 100 trials
Againt AK type hands, we are 52% to win with 88 against AKs, and 55% against AKo. Average it out at say 53% to win.
53 times we win 2700 (143100) and 47 times we lose 2400 (112800) for a net +ve expectation of 30300 over 100 trials or 303 per hand or 1.5BBs.
That compares to 3.2BBs if we got aggressive at two stages rather than 1.
If all of the assumptions are correct then clearly the 2 stage approach is a big winner.
Next is what happens when M drops?
I'll get to that shortly
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Same blind level (100/200), this time you have an M of 6 or a stack of 1800 (9BBs).
When you raise 1/2 your stack you are raising 900 (being 4.5BBs) pot is 1200. A call makes it 2100 and you have 900 left behind you
When you shove the flop you are laying 2.3:1 odds or 43%. Two over cards can profitably call with 24% pot odds but not 43% so you still retain theoretical fold equity over AK. Nothing changes for the higher PPs situation.
So from an M of 6 the 1/2 pot raise and shove still works. However with only a 4.3BB raise, you may get more callers and so the objective of getting it HU might justify shoving from EP.
What about M of 3?
3M stack gives you 900 chips. Half stack raise is only 2.5BBs. Now you are definitely better off shoving.
Seems to be the case then, that from an M of 6 its borderline and somewhat position depended whether you open shove or 1/2 stack raise then shove.
From an M of 8, it seems to be better to 1/2 stack raise and shove
From an M of less than 5, just open shove.
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great thread, great read!!
phaedrus, could i ask you to elaborate on your idea of the "raising half your stack- stop and go".
doesn't that lead to many a situation where you have to call all-in (ugly with 33) or fold away half your stack?
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