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i've been reading a
review of malmuth's poker essays 3 and one point especially troubled me. in his essay
"a note on bluffing", malmuth makes several serious errors when he writes about expected value.
for example, what should you do when you encounter a player who never bluffs? malmuth wrote:
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Since he never bluffs, you should never call. Your expectation on the end is also zero because you never give up a bet that you shouldn't.
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that seems bizzare. just because your opponent bets, it doesnt mean he has a better hand than yours. if i hold the nuts then i'm certainly not going to throw my hand away. instead i'm going to raise back.
has malmuth ever tried to explain his thinking on this particular essay? thanks.
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He's referring to an equilibrium solution. If he doesn't bluff he can only value bet. His strategy will be to bet the top X% of his hands. Since he's betting for value the worst hand he bets must have 50% equity vs. your calling range.
Let's assume:
-the pot contains one unit and will have the option to bet one unit or check after that you may call or fold.
-both your range and his range follow a continuous distribution on the interval [0,1]
Let's say he starts by betting the top 50% of his hands for value. Your strategy should be to call with the top 33.3% of your hands (all these hands have enough equity vs. his range). He'll adjust to you by betting 16.6% of his hands. You'll adjust by calling with only the top 11.1% of your hands. These adjustments continue. And I think you can see where it's headed. Eventually, he'll only be able to bet when he has the nuts and you can only call when you have the nuts (in the case of a continuous distribution this will be never).
The idea is that value bets must be balanced with bluffs (and vice versa).