Playing the odds with Middle pairs.

Here is an excellent discussion about playing middle pairs, when Tournament Indicator shows you are Orange MZoned. The variable involved are seriously endless, but Phaedrus and JSquared try to put this all into numbers...

The problem with orange M is that you can very easily get to pot commitment without betting all that much. When you have small to medium pocket pair (PP) you are either dominated or mostly in a race. Occasionally you will have a hand like Ace rag dominated as well.

From shortish stack, the value of PPs and AK increase while the value of suited connectors decreases. Generally we don't want to be calling raises with a small PP, but raising them first in can be a good steal especially if there are few players left to act where it stands a greater chance that your pair of 3s is not dominated.

So I have spent a bit of time thinking about how PPs can be played to maximum value from Orange M and below.

We know that against a hand like AK the PP is a small favorite over 5 community cards, and that AK is a 70% favorite to miss on the flop.

Now, lets consider a 8M stack of 2400 chips with blinds at 100/200.

If you raise 3xBB (more or less standard raise) to 600 and it is called, the pot will be 1500, and you will have 1800 left. Given your single oponent is 70% favourite to have missed the flop, can you shove any flop with positive EV from this raise?

Answer is no. If you play that approach (raise and shove any flop) from a 3X raise, then AK is getting 180 expressed odds (70% of 600) and implied odds to the value of your whole stack.

That means after 100 hands, you will win 60K (assuming AK correctly folds to a shove when it misses the flop - if it doesn't you actually make more..) But you lose 2400, 30% of the time, for a total loss of 72K. Meaning your shove any flop routine has a negative EV.

What if you make the preflop raise bigger though?

I played around with 4X and 5X, but ultimately it seems to come to a percentage of your stack, not multiple of the BB.

If you raise 1/2 your stack pre flop and shove the rest on the flop, this is what happens when AK or 2 over cards call,

You win 1200x70% and lose 2400x30% of the time, which over 100 trials translates to 84K win and 72K loss.

So that is positive EV, but it is also seems to be about the sweet spot because it small enough to allow AK to fold after the flop.

Going back to the 2400 stack size with 100/200 blinds, your raise of 1200 plus a call, creates a pot of 2700. When you shove the flop for your remaining 1200, you are laying odds of 3.25:1. I.e the pot will be 3900 and it costs AK 1200 to call. Those 30% pot odds are not quite enough to make calling a positive EV play with only 6 outs (of course he might flop more than 6 outs, but those times will be off set when you flop more than 2 outs or flop a set to have AK drawing dead).

So based on the above, it seems to me raising 1/2 your stack with a small to medium PP is about right if your table position is such that you are a solid favourite not to be dominated (i.e earlier the position, the higher the PP you need).