Tinkering With The Nash Equilibrium, Pt. I- Unexploitable Shoving

The situation:  everyone folds around to you in the small blind.  You have 20BBs.  While everyone is confident in their ability to play premium hands heads up out of position, certain hands like weak aces and suited connectors can pose a serious problem, particularly when you are lacking post-flop maneuverability due to your short stack and the inability to launch an elaborate three street bluff.  You can either raise small or limp, though each of them has their own weaknesses.  If you raise small, when you are 3-bet, you will have to lay down a majority of these hands, whether or not you believe that your opponent is bluffing.  Limping will cause a serious imbalance in your range and makes you vulnerable to an in-position opponent whose range is completely undefined.

Two other options remain, and those are folding and going all in.  Since the aggressive move is usually superior, I would opt to go all in.  But which hands are profitable to do so?  A few years back, I was in awe of the Sklansky-Chubukov numbers as outlined in No Limit Hold'Em Theory and Practice.  For those who have not heard, the SC numbers represent the upper limit of your stack size in a $1/2 game where you can move all in from the small blind and have that play be preferable to folding- if you were to flip your hand over first and allow your opponent to play perfectly against you.  

At first I thought this was magic and now I look back at it as being hilariously nitty.  I have since been taught how to use the Nash Equilibrium via StoxEV to shove the highest percentage of hands for the maximum profit.  Though I have no idea how this was solved, I don't need to know how to build a car to drive it, either.

Here are the hands that we can shove for 20BB in a $2/4 game with the rake factored in (which the SC numbers fail to account for).

Not bad, huh?  Now suppose that an astute opponent knows what you are doing and what your precise range is.  How should he defend?

Clearly, there is very little he can do...not to mention that many players are not even comfortable calling with the bottom of this range.  In fact, players can only react to this in one of two ways.  They will either start calling lighter, which is a mistake, or they can call tighter and try and wait you out, making your shoves more profitable.

Although this lesson was fairly remedial, in the next, we will move on to some more advanced related concepts and you with then really begin to see just how deep the rabbit hole goes....