Week 8 Problem Session: Exploitability workshop

Computing best responses and exploitability numbers for opponent frequencies not covered in lecture, to check the formulas generalize

12 April 2027

Before the session#

Read the lecture page. Bring the $25-per-hand exploitability number for c = 50% — the session computes it again from the formula, then at new values of c nobody has seen yet.

In the session#

Everyone computes the pure best response to several villain bluff frequencies scattered around x* = 25% (both above and below), checking in each case that the equilibrium 66.7% mix is not the best response against a known fixed x — and that only right at x* does the mix become correct.

Second half: exploitability computed at several hero calling frequencies, plotted by hand as a function of c, to see the zero point land exactly at c* and the line’s slope directly reflect the bet-to-pot ratio.

Afterwards#

Nothing is marked this week. Going into week 9: comfort with the distinction between “the equilibrium mix” and “the best response to a known, fixed opponent,” since week 9 asks which of week 7’s and 8’s results even survive with a second opponent added to the pot.