Re: Cross-post from NL Hold\'em Forum: Conceptual Big-Bet Hand
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Hero and Villain (both good players) are heads up on the flop with villain on the button and $100 in the pot. Both players each have $1000 more behind.
Flop is T53 - all hearts.
Hero leads for $100 with KhQh and villain raises to $400 with AhTs
Should hero reraise all-in or flat call and then lead out all-in on any non-heart turn card? Assume villain will probably call a flop reraise but will probably fold to a turn all-in.
Clearly villain has made a mistake by raising on the flop. However, once that has happened, if hero reraises all-in, villain is making a mistake by folding (i.e. - hero would want villain to fold to the reraise but would want him to call a big turn bet). Or is it the effective odds that are important here?
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First - assume the flop is 9 high so villian can't hit a running boat...
If Hero pushes on the flop then the villian will fold and the Hero ends with $1500 ($1000 he had at the flop + $100 previously in the pot + Villian's $400 raise).
If Hero calls then:
There is a 7/45 chance that a heart falls. If the Hero folds here, he ends at $600 (out the $400 he put in on the flop).
There is a 38/45 chance that a heart does not fall. In this case, we assume the Hero pushes for $600 more and the Villian calls. This brings up two possibilities:
1) there is a 7/44 chance a heart rivers and the hero goes broke (ends at $0).
2) there is a 37/44 chance that the river is a blank and the hero ends at $2100 ($100 in pot preflop + $800 put in pot on flop + $1200 put in at the turn).
Expected Stack Size: (7/45)*(600) + (38/45)*(7/44)*(0) + (38/45)*(37/44)*2100 = 1584.55.
So if Hero smooth-calls, he can "expect" to have $1584 at the end of the hand, versus $1500 by raising the flop. Hence, in the long run calling is better.
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