The Game Plan

Quantifying blocker considerations

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Quantifying blocker considerations

I have an idea for how we can quantify the EV-value of optimally considering blocker effects at certain nodes. I'm not sure of this sort of analysis has been done before, but I would be very curious to see the results if someone can carry out the details.

Consider an IP river spot where GTO dictates check or jam. The GTO strategy will be optimal in its blocker considerations when choosing the bluffing portion of its jamming range. A solver can give you the EV of this spot, which I'll call X.

My idea is to construct a strategy which matches the high level parameters of the GTO strategy, but which is blocker-oblivious. My idea for constructing this strategy programmatically is as follows. First, identify all N hands whose jamming-EV against a GTO opponent is negative when called - these we will identify as bluffing candidates. GTO allocates a certain amount of jamming probability mass to these hands - zero to some, and nonzero to others. Next, we will redistribute that probability mass distribution to be uniform across the entire set of N bluffing candidates. And that is our blocker-oblivious strategy. Note that this strategy matches the high level parameters of GTO: it jams with the same frequency, and it has the same value:bluff ratio. But by jamming with equal probability with all its bluffing candidates, the strategy is blocker-oblivious.

We can analyze the EV of this strategy in two ways. One is to fix the OOP calling range to be GTO. The other is to set the OOP calling range to be maximally exploitative of our constructed strategy. I'll call these EV values Y and Z, respectively. Both make some sense to use as a comparison. I'm not familiar enough with solver software to know the feasibility of either computation.

The differences, (X-Y), and (X-Z), can be interpreted as the EV gained by incorporating blockers, against a stationary GTO opponent and against an exploitative opponent, respectively.

Extending this approach beyond IP river check/jam scenarios gets hairy.

The practical value of this sort of study would be understanding how much of the value of a GTO strategy comes from optimal choices of action frequencies and value:bluff ratios, and how much comes from allocating hands to actions, using blocker considerations.

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