Bad beat --- EV vs. Risk

[PrayingMantis]

After this little bad-beat, I had some thoughts about EV and risk, and got to some interesting conclusions.

The hand:

22$ 2-tables, blinds 25/50. I'm UTG w/1400, holding A /images/graemlins/spade.gif A /images/graemlins/diamond.gif, I raise to 150. MP (5000) calls, BB (2200) calls too.

Flop: 7 /images/graemlins/spade.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/diamond.gif (pot: 475)

BB checks, I bet 400, MP calls, BB calls.

Turn: 8 /images/graemlins/heart.gif (pot: 1675)

BB checks, I push for 850, MP calls with A /images/graemlins/heart.gif T /images/graemlins/heart.gif. BB folds.

River: 9 /images/graemlins/heart.gif.

We usually say after such beats, things like "you want him to call you, this is great for you, etc.". While this is of course true in a sense, I figured that if you consider it strictly in EV vs. Risk terms, you *don't* want him to call here with his hand.

Calculation:

My CEV for him calling: (0.8*2525)-(0.2*850) = +1850, with 20% risk of busting .

My CEV for him folding: +1675, with 0% risk of busting .

So, I gain only 175 chips more, for this 20% risk of going bust.

I would much rather he *wouldn't* call me here.

All this may not have clear practical side, since I will push here every time. However, I certainly feel different now about "what I want my opponent to do".

Any thoughts?

[Bigwig]

[ QUOTE ]
After this little bad-beat, I had some thoughts about EV and risk, and got to some interesting conclusions.

The hand:

22$ 2-tables, blinds 25/50. I'm UTG w/1400, holding A /images/graemlins/spade.gif A /images/graemlins/diamond.gif, I raise to 150. MP (5000) calls, BB (2200) calls too.

Flop: 7 /images/graemlins/spade.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/diamond.gif (pot: 475)

BB checks, I bet 400, MP calls, BB calls.

Turn: 8 /images/graemlins/heart.gif (pot: 1675)

BB checks, I push for 850, MP calls with A /images/graemlins/heart.gif T /images/graemlins/heart.gif. BB folds.

River: 9 /images/graemlins/heart.gif.

We usually say after such beats, things like "you want him to call you, this is great for you, etc.". While this is of course true in a sense, I figured that if you consider it strictly in EV vs. Risk terms, you *don't* want him to call here with his hand.

Calculation:

My CEV for him calling: (0.8*2525)-(0.2*850) = +1850, with 20% risk of busting .

My CEV for him folding: +1675, with 0% risk of busting .

So, I gain only 175 chips more, for this 20% risk of going bust.

I would much rather he *wouldn't* call me here.

All this may not have clear practical side, since I will push here every time. However, I certainly feel different now about "what I want my opponent to do".

Any thoughts?

[/ QUOTE ]

Of course when you are up against the chip leader, sometimes your max bet isn't enough to force him out of calling because of the odds he's getting. That's what happened here. But your assessment of EV and risk is correct. Hopefully, the probability of him folding is great enough that it makes it worth it.

[Peter Harris]

you are, of course, absolutely correct.

S&M mention this in Tournament Poker for Advanced Players. Anyone who hasn't read it, do so!

that book was invaluable for my tournament play, it's without a doubt the best tourney book available.

Unlucky river, buddy.
Pete

[Jonathan]

[ QUOTE ]
[ QUOTE ]
After this little bad-beat, I had some thoughts about EV and risk, and got to some interesting conclusions.

The hand:

22$ 2-tables, blinds 25/50. I'm UTG w/1400, holding A /images/graemlins/spade.gif A /images/graemlins/diamond.gif, I raise to 150. MP (5000) calls, BB (2200) calls too.

Flop: 7 /images/graemlins/spade.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/diamond.gif (pot: 475)

BB checks, I bet 400, MP calls, BB calls.

Turn: 8 /images/graemlins/heart.gif (pot: 1675)

BB checks, I push for 850, MP calls with A /images/graemlins/heart.gif T /images/graemlins/heart.gif. BB folds.

River: 9 /images/graemlins/heart.gif.

We usually say after such beats, things like "you want him to call you, this is great for you, etc.". While this is of course true in a sense, I figured that if you consider it strictly in EV vs. Risk terms, you *don't* want him to call here with his hand.

Calculation:

My CEV for him calling: (0.8*2525)-(0.2*850) = +1850, with 20% risk of busting .

My CEV for him folding: +1675, with 0% risk of busting .

So, I gain only 175 chips more, for this 20% risk of going bust.

I would much rather he *wouldn't* call me here.

All this may not have clear practical side, since I will push here every time. However, I certainly feel different now about "what I want my opponent to do".

Any thoughts?

[/ QUOTE ]

Of course when you are up against the chip leader, sometimes your max bet isn't enough to force him out of calling because of the odds he's getting. That's what happened here. But your assessment of EV and risk is correct. Hopefully, the probability of him folding is great enough that it makes it worth it.

[/ QUOTE ]

But thats not what happened here. In this case, MP is putting in 850 to win 2525. This is less than the 4.1 : 1 odds dictated by his flush draw. So he is getting insufficient odds to call this bet.

For him to call the bet is a mistake, and for him to fold is correct play. You profit when your opponent makes mistakes, and fail to profit when your opponent plays correctly. So by Sklansky's fundamental theorem of poker, you should want him to call here.

Of course, if a /images/graemlins/heart.gif is coming off the deck, then thats another matter /images/graemlins/cool.gif

Regards,
Jonathan

[PrayingMantis]

[ QUOTE ]
But thats not what happened here. In this case, MP is putting in 850 to win 2525. This is less than the 4.1 : 1 odds dictated by his flush draw. So he is getting insufficient odds to call this bet.

[/ QUOTE ]

This is not accurate. From his point of view, he did have about the right odds to call, unless he puts me specifically on AA, (or better than pair, which is not very reasonable with this board). If I hold any over-pair (99-KK) he's getting quite the right odds, not to mention the option I'm bluffing with Ax - in that case he gets even good odds.

So from his point of view - he is, probably, getting the odds.

[ QUOTE ]
For him to call the bet is a mistake, and for him to fold is correct play. You profit when your opponent makes mistakes, and fail to profit when your opponent plays correctly. So by Sklansky's fundamental theorem of poker, you should want him to call here.


[/ QUOTE ]

Again, this is not quite accurate. As I showed in the original post: with the hand he *actually* holds, I prefer he *wouldn't* call me, as it will increases my risk dramamtically without increasing enough CEV. If it was ring game, then the fundamental theorem would kick in, and I *would* want him to make the mistake of calling, since $EV is all that matters.

There are tournament situations, in which your opponent might make a mistake (FTOP-wise), but you prefer he woudn't do it, because it will put you in greater risk than if he did the "right" thing (objectively speaking, knowing what we both hold) , i.e., folding here.

[Guy McSucker]

[ QUOTE ]

I gain only 175 chips more, for this 20% risk of going bust.

I would much rather he *wouldn't* call me here.


[/ QUOTE ]

I think that's right.

You can also factor in the Malmuth point that the chips he stands to lose are worth less than those you are risking, since he has a big stack. Whatever stage of the tournament you're in, this holds true in this case, since he has 5000 out of 27000 in play, i.e. a large proportion of the total.

So although his call is marginally negative EV (175 chips), it's probably more or less neutral or even positive in money terms, given his large stack. You would definitely prefer a fold.

I believe your conclusion holds even if he has a stack the same size as yours, since the risk outweighs the reward here, but I thought I'd mention this extra point anyway.

Guy.

[kiemo]

[ QUOTE ]

You profit when your opponent makes mistakes, and fail to profit when your opponent plays correctly.



[/ QUOTE ]

Unless your in a tournament and his mistake knocks you out.

His odds may not have been perfect, but he was chip leader and he had a chance to knock another player out of the tournament, which is a two-fold benefit for him.

Often times in tournaments the FTOP simply doesnt apply. See: Possibly folding AA preflop agaisnt 2 all-in players whom have you covered with 4 players left in a 3 position paying tourney.

[Jonathan]

OK.... I now agree with both you and PrayingMantis. I failed to take proper account of the tournament context.

Thanks for the clarification.

By the way, what is the "C" in CEV?

Thanks,
Jonathan

[PrayingMantis]

[PrayingMantis]

[ QUOTE ]
You can also factor in the Malmuth point that the chips he stands to lose are worth less than those you are risking, since he has a big stack. Whatever stage of the tournament you're in, this holds true in this case, since he has 5000 out of 27000 in play, i.e. a large proportion of the total.



[/ QUOTE ]

I agree. Another point is that the +175 I "gain" if he calls, come on top of +1675 I "already have", if he just folds. So, according to the same logic, by which the more chips I have the "less" they worth, these 175 actually worth less than their concrete value (comparing to the rest of my profit here), while my 20% risk of busting if he calls remain the same. This makes his call even less favorable for me.