Tuesday, April 24, 2007

SNG Strategy - The Push Over Limpers

One of my favourite 'moves' today, something that should really be in every lower limit SNG players SNG Strategy arsenal... the good 'ol fashioned shove over limpers.

After doing some thinking about this one over recent days I am starting to be concerned that I could actually be doing this with the wrong hands - will look at some numbers in a bit, first a description...

The usual timing for this move is levels 4 or 5 on Stars (BB100 or 150), with a stack of 1200ish (have been super tight early as usual) and one of the last to act... you see a couple of limpers ahead from the button (for example) and look down at something like AJs or 99 - Boom, you shove and pick up 350 to 500 from the pot without a fight - some great ammunition for the later stages with relatively little risk.

Now, my thoughts are these - since you do not get called that often here (especially if you have folded every single hand up to this point!) does the strength of your holding make an ev difference... the question is whether it is actually a waste of a medium strength hand to shove here?

First let us discount a few things... I will assume only a 2-3% chance of either blind waking up with a monster... will also assume that none of the original limpers are either very large stacks or very small stacks (and thus more willing to call).

The key questions then becomes these:

1) How often am I called?
2) What equity does my hand have when called?

1) How often called... this of course depends on many factors, including the level at which you are playing and the experience of the players who limped. The limp itself implies no monster hands are against you on the most part - but this can not be entirely discounted, people at all levels limp aces after all.

Here are some summed probablilities to work with...
- Combined chances of blinds calling - 5%
- Probability of first limper calling - 10%
- Probability of 2nd limper calling - 8% (limping behind less likely to be a callable hand)

Sum in this case - discounting 2 or more callers = 23%

So, 77% of the time we win 500 chips with no further action (when BB=150)... all good, but incomplete since we sometimes win when we are called too...

2) Equity when called.... now we have to work out the ranges of calling hands. At the lower limits $27 and below this can be fairly wide... going to say pairs above 77, AKo and AQo+... for the sake of argument.

Our equity against this range with the 2 candidate hands:

99 = 44%
AJs = 36%

So when called with the 99 we are in good shape having 44% winning chances. The overall equity (working with chip equity here rather than $equity) is. So over 100 attempts:

77 times we win 500 without a showdown = 38500
23 times we are called.
- 12 times we lose all 1200 = -14400
- 11 times we win 1200 + 350 from the other limper + blinds = + 16830

So on average we end up with 409 more chips than we started with... now that is one hell of a positive equity move!!

Same sum with the AJs

77 times we win 500 - +38500
23 times we are called
- 16 times we lose 1200 = -19200
- 7 times we win 1550 = +10850

Again we end up with a positive expectation - this time +301 chips per try.

So now we get to the crunch point - with only 36% equity vs opponents range we still win money... what equity when called do we need to show a loss... so now the same numbers but with us holding 72 off!

Equity when called vs opponents ranges = 20%

77 times we win 500 - +38500
23 times we are called
- 18.5 times we lose 1200 = -22200
- 4.5 times we win 1550 = +6975

We still win! This time our expected gain is 232 chips - and that is a huge percentage of our 1200 stack.

The significant number here is the percentage of times we get called... if we increased this to say 30% or 35% then the lowest showdown equity hands may start to show a loss. The actual chances of a call are of course a judgement based on player tendencies and stack sizes. However only the least observant opponent would not notice you folding 25 hands in a row then suddenly shoving.

Ok, so I have been wasting my meduim strength hands by shoving over limpers... next time it will be junk!

GL at the tables - and if I see you shoving over my limp I'll call (!)

Cheers, Mark


Littleacornman said...

Great stuff as always Mark.The % chance of a villain waking up with a monster was intresting.I feel my game is at it's best if I'm struggling to get chips but have the confidence to raise with air.Gave me some food for thought with regard to that.

Thanks again

JB1795 said...

Well written. Found your link from the Cardplayer forums. I think you can even raise the equity of 99 against the range of hands that limp-call. While it's true players limp with Aces or Kings, they're less likely to limp with TT-QQ (since these pairs are more vulnerable). It's also true there are more ways of dealing AK/AQ than AA/KK.

Therefore I think you're facing a slightly weaker range the times you do get called.

Pocket nines have, for example, 62% equity against a player who limp-calls with 77, 88, AQ, AK, or AK suited. Any thoughts?

Mark said...

Good points JB, One other thing to factor in is that there is always a chance of a 'donk call' - just the other day someone limp / called my push with K9s... I was 70% in this hand so all good but does emphasise the big difference between what you think people will call with and the reality at the table (this was a $27)....

Cheers, Mark