[Jerrod Ankenman]

[ QUOTE ]
Starting on page 272, for NL hold'em, the authors describe an optimal strategy on the flop OOP and facing a preflop agressor.

What I understand is:

1)on the flop we check 100% of the time even against opponents who don't autobet.
2)as a consequence, betting on the flop is a dominated strategy so we never bet into our opponent.

Am I right?

[/ QUOTE ]

The strategy we outline is not optimal! If we had an optimal strategy for NL holdem we sure wouldn't publish it in a book. Instead, it's a case study of applying the principles of optimal play to an actual game. So hopefully the strategy is at least sorta balanced and not that exploitable.

In the case we describe, it's a multiplayer scenario (as there is an "early" raiser) which further prevents there from being an "optimal" strategy.

In any event, supposing that we treat the hand from the flop on as a headsup game where the opponent has some fixed distribution, our contention is that an early raiser in NL playing against the blind should probably autobet as his strategy on the flop (as an equilibrium). If this is the case, then likewise the blind should autocheck to the bettor. This is true regardless of who the player is or what weaker strategy they will employ -- if autobetting and autochecking are the ~optimal strategies, then the raiser can't improve by checking on the flop.

But betting out is not necessarily dominated - in order for that to happen, checking instead of betting would have to have higher or equal expectation against every possible opponent strategy, which is not the case. For example, suppose the opponent played normally if you checked, but automatically folded unless he had the nuts if you bet. Obviously this is a stupid strategy, but betting out would be superior in this case. It's that against the ~optimal strategy, checking has a higher or equal expectation against the opponent's optimal strategy than betting -- hence we check all hands.

That make sense?

Jerrod