Conceptual 5/10 NL Hand - tying together stack depth/stop'n'go

[GFunk911]

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Assume villain will probably call a flop reraise but will probably fold to a turn all-in.

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A non-heart will come 84% of the time, hero pushes and villian folds, netting 450 for hero.

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Intuitively, this makes sense, since your opponent will never fold.

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Both our answers are correct, you're just solving a different problem.

[C Dubya]

If I am wrong here, I'd appreciate some feedback (I'm relatively new but I enjoy trying to figure these things out). I am assuming the following: Each player knows the other's cards. The flop is the decision point, all calculations are based on what happens from that point on.

Strategy 1 - Hero raises all-in on the flop. If he wins the pot, he profits by 1200. When he loses, he is out 900. According to twodimes.net, hero wins .683 of the time. Hero's expectation for this strategy is .683 X 1200 - .317 X 900 = 534.50.


Strategy 2 - Hero flat calls 300 on the flop and one of the following happens.

A. Hero folds when a heart hits (7/45 of the time or ~ .156. His expectation is .156 X -300 = -46.80.

B. Hero bets all-in and villian folds when an ace or a blank hit (36/45 of the time or .8. Hero's expectation is .8 X 600 = 480.00.

C. Hero bets all-in when a ten hits. A ten hits 2/45 of the time or ~ .044. This requires additional calculation because villian now has the odds to call. According to twodimes.net, hero wins .614 of the time when a ten hits. Hero's expectation when a ten comes on the turn is .044 X (.614 X 1200 - .386 X 900) = 17.13.

Add the expectations for Strategy 2a, 2b, and 2c. The total expectation for strategy 2 is 450.33.

Thus betting all-in on the flop is superior to calling and then taking one of the three prescribed actions.

[GFunk911]

I didn't run through your math c dubya, but your ligic is impeccable, awesome job

[togilvie]

You're right - I had mixed this up. But it simply makes the Stop and Go more attractive. Hero wins 900 in this instance.

[coltrane]

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if hero reraises all-in, villain is making a mistake by folding

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villians fold wouldnt be incorrect if he knew he was only drawing to his heart outs. unless you arnt assuming that?

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yes it would be incorrect....at that point the bet would be $600 to villain with $1500 in the pot......he's getting 2.5 to 1 on a 2 to 1 shot.....

[coltrane]

togilvie,

I believe something is not quite correct with the math on your tree.....the total equity for the flop reraise is higher than what you have shown....great diagram though....

[coltrane]

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So, in this specific situation, you want to get your money in on the flop (this hand shows why you don't want to get yourself pot-stuck on a draw). But, of course, change a few details, and the answer will change...

ML4L

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care to elaborate?.....hero is not drawing, so are you saying villain doesn't want to be pot-stuck? (and is there a measuring stick you personally use to define "potstuck"?)....I agree it's better for hero to get the money in on the flop, but I think it's purely for EV reasons.....

I appreciate yours and all the other responses.....here's what I have seem to come up with....it's interesting because even in this very mathematical hypothetical situation, there seem to be some player-dependent variables......if there's even a slight chance that villain would call on the turn (i.e. - if we say he's not quite as good of a player as in the original post), it becomes a higher EV play for hero to stop'n'go.....I wouldn't have thought that.....my general feeling in these types of situations is always to push on the flop if I'm hero....however, even though villain has made a mistake by his flop semi-bluff raise, he's not making a mistake by calling the reraise - BUT, he's making an even bigger mistake if he calls on a blank turn push......so, if I'm hero and I think there's a chance my opponent will call my turn bet on a blank, the stop'n'go actually becomes a better play - which I wouldn't have thought......

[GFunk911]

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You're right - I had mixed this up. But it simply makes the Stop and Go more attractive. Hero wins 900 in this instance.

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Your chart is wrong. The "correct" way to think about EV is with all the money in the pot as not yours anymore, but it's often easier to use a different point of reference when calculating. However, you need to use the same one throughout. For example, on a flop all-in, you have the value of winning the showdown as 2100 (the aamount of chips you will have as the end, assuming both players started with 1050), yet the EV of losing a showdown as -900 (the amount of chips you will lose as compared to folding to the turn raise). The proper numbers would be 2100 and 0. Continuing to use the total number of chips at the end of the hand as the EV, Heart Turn - Check and Fold should be 600, Non-Heart Turn/All-In/Win should be 2100 (as you have it) and Non-Heart turn/Allin/Lose should be 0 again. See other posts in this thread for an explanation of the EVs, assuming the villian folds a non-heart turn

[coltrane]

incidentally, here's my math on the situation:


if hero reraises flop, he is 68.3% to win $2100 which is an EV of 1434

if hero waits til turn:
1) he has an EV of 600 (his saved turn bet) when a heart falls and he check/folds (this happens 7/45 times)
2) he has an EV of 1289 when a ten falls and his turn all-in is called by villain (2/45 times)
3) he has an EV of 1500 when any other card comes and villain folds (36/45 times)

total EV for waiting til turn: 600*(7/45) + 1289*(2/45) + 1500*(36/45) = 1350

EV is higher if hero pushes flop....


if villain called when an ace came on the turn (which would be a mistake), the turn EV for hero now becomes.....

600*(7/45) + 1289*(2/45) + 1575*(3/45) + 1500*(33/45) = 1355

again, still better for hero to push flop....

[Mike Haven]

i posted these two sets of comments against your post in the probability forum, but this discussion seems far more interesting and active:

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

addendum:

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