Theory - AK limp push unexploitable?

[excession]

[kennyg]

[excession]

Kenny - on a 6 max table UTG and UTG+1

OK - bit of a rush post over lunch and not great use of terms, confusing two issues.

1. There is the first question - 'is it better EV than playing AK UTG and UTG+1 in a more 'standard' manner'.

2. Is the overall strategy of doing this with AA, KK and AK 'exploitable'?- if your opponents work what you are doing can they alter their play to make it -EV for you? (or given that they are going to have their work cut out to make it -EV with such strong starting hands - can they adjust to seriously lessen your overall +EV?)


Let's do some back of the envelope maths..

First just looking at AK.

You are really only worried in EV terms about AA or KK calling you, but let's look at the full range of callers:

AA 3 ways (you have an A of course)
KK 3 (and a K)
QQ 6 (but let's say 1 would fold = 5)
JJ 6 (but let's say 3 would fold = 3)
AK 9 (lets' say 5 would call)
AQ 12 (let's say 3 would call).

Maybe you would get a few donk calls with lower Ax or TT and below but let's assume that those would cancel each other out and the above is a reasonable calling range.

So how often will the LP raiser have a calling hand?

I think a very reasonable raising % for CO or Button on a normal 6 max table with one limper in is 20% - that is the LP raiser is likely to raise with any of the top 20% of hands. Even if he doesn't think I'll fold he will want to try and isolate me OOP. I think a call behind is also going to be in top 20% but he is very unlikely to not re-raise with AA,KK,QQ,JJ or AK. So a cold call usually (lets' say 75% of the time) means you can stop worrying about these hands unless he is very tricky.

So let's look at the simplest scenario where we limp, get a button raiser to 4BB and it's folded back to us. We push with AKo. There is 6.5BB in the pot.

We estimate his calling range at 22 hands of the 1326 (see above).
We are 93/6 dog to AA x3 (18/300)
We are 70/30 dog to KK x3 (90/300)
We are 57/43 dog to QQ and JJ x8 (344/800)
We are tied vs AK (small dog if AKs) x5 (235/500)
We are 73/22 favorite vs AQ x3 (219/300)

So if called by his likely range we are 906/2200 or 41% (50% would be a coin-flip). Also there is a little money already in of which you have a 41% share.

But if he is raising in LP with any hand in top 20% (265 hands or so) but throwing away all but 22 of the to a push then we are making 6.5BB (of which 5.5BB is profit for us), 11 times for each 12th time we get called.

So we make 60.5BB profit for each time we get a caller. And when you do you are going to end up no worse than 40/60 overall against their range with a small pot sweetener already in. Even if the lower stack was 200BB you would win back 165 on average if you got called (sowhen you add on the 60.5BB made you are still up).

Even at 300BB you still end up +$12.5 on these figures (as opposed to folding) - when you are that deep alternative strategies for both players seem more attractive. You'd think this would be especially true if because of the deep stacks the caller tightens up his range to AA and KK.

But let's just run that for a second to see if we can exploit the strategy by only calling with those hands.

Only 6 ways to make AA or KK. 259 folds for 6 calls. You get called once every 44 times. 43x 5.5 = $236 profit. And even against the range of AA and KK you are 18% to win - (+$108) - so in fact tightening up when 300BB stacked against someone using this strategy with AK would be worse than just calling off as if you were 100BB stacked.

Now looking at the 3 handed situation you will get more callers - but not twice as many - as the pre-flop cold caller likely doesn't have a premium hand. Let's say you get one call in 9 now. But the money you have made from the blinds is 8.8x8 or 68BB - so the push is looking even better 3-handed because of the extra money in the pot.

Now in fact on the donkey tables I play on calling is much more frequent (encouraged no doubt by my 50% buy-in) but as thay call with A-junk (which I dominate) as much than with medium pairs - this actually increases my EV..I also increase my EV by just folding out the AK when very tight players raise behind me (as in 3% PFR and below). I also add may QQ or even JJ to the mix of limp/push hands when I have tilters or maniacs in LP.

I should also add that I usually limp with any pair below JJ and very occasionally medium suited connectors in EP as well so they can't assume they will be getting a push if they raise me from LP.

OK let's try exploiting it another way - you see what I am doing so you call with any pair - as they are favorites vs AK and there is money in the pot. Fine, except that 43% of the time when I limp/push it's AA or KK you'll see and not AK. Not so smart now...

Can you exploit by just folding? Well not unless you want to give me a easy run with my small pairs and suited connectors (which I will play more often if I'm getting to see cheap flops easily).

What about limping behind? Well that might be best all told - but on a normal 6 max table someone else behind may pop in a raise anyway..so I'm not sure it badly effects me...I guess if I don't push when the guy behind you raises you can usually rule out me having AA,KK or AK, which may be of some use if you feel able to call the raiser or are brave enough to push yourself.

The biggest downside is whether I lose more EV with AA and KK playing them this way than by putting in a 'normal' raise. My experience is that the limp/push isn't a bad way to play AA/KK anyway for EP although a limp-re-raise is likely optimal in aggro 6 max. I think though (esp if you buy in short like me and there isn't much difference between and push and big re-raise) that the improved returns for AK will more than make up for it.

I haven't got many stats to back this up as I've only consciously started doing this in the last couple of weeks but would be grateful for any thoughts/feedback.

cheers

[WayToGo]

[k3nt]

[excession]

[Alastor2262]

130k+hands DB : nl50 nl100 nl 200 4-6 handed.
UTG : 6266
AA(33) : 12.24 ptbb
AKs(14) : 0.45
AKo(77) : 0.47
KK(23) : 4.05

UTG+1 : 18615
AA(85) : 1.85
AKs(67) : 0.77
AKo(176) : 0.53
KK(81) : 5.31

[excession]

Q's of the top of my mind:
- What if UTG+1 raises BB folds? (i call.)
-What if UTG+1 raises BB calls LP calls and SB calls? (i call)
-What if LP raises but blinds both fold. (i reraise)
-What if the LP raiser is very tight. (4% PFR) (i call/fold 80/20)
-What if everyone folds and the BB raises.

1. Depends on how often UTG+1 opens for a raise in that position (with 100BB stacks I suspect you are OK to push if he is no tighter than say top 10% here) - would need to do calcs..let's see..
22 calls out of 132 hand = 22:110 call/fold ratio. 110 Folds net you profit 605BB (715 for EV calcs if you count the 1BB you have put in); 22 calls net is -300BB - so you are showing a profit of about 2.3BB/hand (1.15PTBB/hand) by pushing here..if you can beat that flat calling then I guess you do that..

2. Likely LP and SB don't have premium hands - maths say push unless UTG+1 is very tight
3. push
4. fold as OOP
5. push

[shobute]

[excession]

[WayToGo]

[excession]

[NorthView]

Seems a good way to deal with the perennial AK OOP problem. AA/KK are often pretty tricky to play OOP post flop against a decent floater, too.

You'll get added value in cases when you limp, OTB raises, SB or BB call, you push, and the LP raiser who's unaware of your range, puts you on a resteal and calls with inferior holdings.

[Aisthesis]

[Aisthesis]