Cross-post from NL Hold'em Forum: Conceptual Big-Bet Hand

[coltrane]

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?

[Mike Haven]

if hero reraises, villain would be correct to call with two cards to come, and hero would lose $600 if a heart fell on the turn

if hero waits for non-heart turn to push all in, villain would be making a mistake in calling with only one card to come, and assuming hero folds if a turn heart falls he would not lose his $600

[Mike Haven]

i've now done my math on this and i was wrong, previously, in "actual dollars won" terms:

if hero calls then 308 (7 x 44) times out of 1980 (45 x 44) hero will lose 300 = 92,400 (assuming hero folds if heart turns)

if hero bets non-flush turn all in then 1672 (38 x 44) times out of 1980 he will win the 300 = 501,600 (assuming villain folds)

net win = +409,200 or +207 per hand

if hero raises all in then 308 (7 x 44) times out of 1980 (45 x 44) hero will lose 900 = 277,200 on turn (assuming villain calls)

and 266 (7 x 38) times out of 1980 hero will lose 900 = 239,400 on river

and 1406 (38 x 37) times out of 1980 he will win 900 = 1,265,400

net win = +748,800 = +378 per hand

therefore it is "better" to push all in on the flop

my previous answer seems to give the "right" answer if you look at "dollars won per dollar staked":

you win $207 for a stake in play of $300

or you win $378 for a stake in play of $900

i suppose the yardstick of poker is "actual dollars won"

however, if you didn't want to run the risk of losing a number of $900 stakes before the "long run" cut in, then winning $171 less for stakes of only a third the size of $900 might still be regarded as the prudent way to go, for those on a limited bankroll

[elitegimp]

[ QUOTE ]
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?

[/ QUOTE ]

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.