Baby flush vs. slowplayer

[danzasmack]

This guy has a very low pfr and I've played with him a good amount. He likes to open limp big hands and bad hands alike, and get creative on big streets with them, a lot of times waiting for the river.

This may be really simple but I'm just running through the "types" of players I've been up against lately.

So this guy limps UTG and it's folded to me in the BB with 4[img]/images/graemlins/heart.gif[/img]5[img]/images/graemlins/heart.gif[/img]. I check.

Flop Q[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/club.gif[/img]

Check, check.

Turn 3[img]/images/graemlins/heart.gif[/img]

I bet, he raises, I call.

River 2[img]/images/graemlins/heart.gif[/img]

All streets up for debate. Bet the flop and quit on the hand? Turn line? River - bet/call, check/call, check/raise/call? No folds.

[Gildwulf]

bet/call river, looks pretty standard other than that

[Grisgra]

[ QUOTE ]
bet/call river, looks pretty standard other than that

[/ QUOTE ]

In what situations is bet/call better than a checkraise?

[MarkD]

"Are we ahead >60% of the time?"

Gris,

You've mentioned this twice in the past two days with regards to river analysis. I know I know where this is from but I can't think of the source and I'm having problems deriving this number. What is this a reference to and where is the source?

[Guy McSucker]

[ QUOTE ]
"Are we ahead >60% of the time?"

Gris,

You've mentioned this twice in the past two days with regards to river analysis. I know I know where this is from but I can't think of the source and I'm having problems deriving this number. What is this a reference to and where is the source?

[/ QUOTE ]

I think it's nothing more than the idea that you will put in three bets when you lose and two when you win.

I'm not convinced it's 100% correct because you lose a lot of value when the river gets checked through: betting and getting called is worth a lot, almost a whole big bet I suppose, but each successive bet that goes in has a little less equity for you, especially the third one.

Guy.

[MarkD]

[ QUOTE ]
[ QUOTE ]
"Are we ahead >60% of the time?"

Gris,

You've mentioned this twice in the past two days with regards to river analysis. I know I know where this is from but I can't think of the source and I'm having problems deriving this number. What is this a reference to and where is the source?

[/ QUOTE ]

I think it's nothing more than the idea that you will put in three bets when you lose and two when you win.

I'm not convinced it's 100% correct because you lose a lot of value when the river gets checked through: betting and getting called is worth a lot, almost a whole big bet I suppose, but each successive bet that goes in has a little less equity for you, especially the third one.

Guy.

[/ QUOTE ]

Guy,
You are absolutely correct. But, if you ignore betting out and only compare c/c vs. c/r we can analyze that case. Trying to analyze the case where we bet out and get called and raised vs our opponent checking behind a hand that would have called our bet adds a lot of complexity. I've provided a full analysis of c/c vs c/r now that I understand the number Gris was using, but I will avoid trying to analyze the betting vs. checking question for now as I'm feeling too lazy.

[Grisgra]

[ QUOTE ]
"Are we ahead >60% of the time?"

Gris,

You've mentioned this twice in the past two days with regards to river analysis. I know I know where this is from but I can't think of the source and I'm having problems deriving this number. What is this a reference to and where is the source?

[/ QUOTE ]

I think my math is a little off on this relative to the best alternative (check/call), but let me explain what I was thinking:

I ran through the math in the other thread on this -- has to do with checkraising/calling a 3-bet vs not. If villain auto-bets, and we checkraise, auto-call a 3-bet (even if we know we're beat, bcs, hey, pot is big, durrrrrrr):

60% of the time we win 2 bets this way (0.6 * 2 = 1.2bets +EV)
40% of the time we lose 3 bets this way (0.4 * 3 =-1.2bets -EV)

So it's neutral EV at the 60% mark with our assumptions.

At the 60% mark, though, check/call gets us a little profit -- 0.6 * 1 - 0.4 * 1 = 0.2BB/hand. So at 60%, check/call is better than checkraise/call a 3-bet.

At the 70% mark:

0.7 * 2 - 0.3 * 3 = 0.5BB/hand for checkraise/call 3bet
0.7 * 1 - 0.3 * 1 = 0.4BB/hand for check/call.

So I have to take back what I was saying -- the break-even point for checkraise/call 3-bet vs check/call is about 67%. Unless I messed up my math again [img]/images/graemlins/smile.gif[/img]. If the villain may 3bet with a worse hand some small proportion of the time (and we think he will, which is why we call the 3-bet) then things lean slightly more in favor of the checkraise/call a 3-bet line.

Where is Cartman when I need him?!

[Victor]

i cant imagine why we wouldnt cr here.

[MarkD]

Ok, after seeing your math now I get the 60% number. For some reason when I read your initial posts I thought, "Shouldn't that be 67%?" but didn't really know what you were looking at.

The break even point is exactly 2/3 or 67%.

Eq 1: 2*z - 3*(1-z)
Eq 2: z - (1-z)

Set eq 1 = eq 2 and solve for z.

Now, if you want to investigate the effects of the small percentage of the time that we get 3-bet on the river by a hand we beat then the equations will be:

X = percentage we are ahead but he won’t 3-bet our check raise
Y = percentage we are ahead and he 3-bet’s our check raise

Eq 3: 2x + 3y – 3*(1-x-y)
Eq 4: x+y – (1-x-y)

Set 3 = 4 gives us:
3x + 4y = 2
or:
x = 2/3 – 4/3y
y = ½ - 3/4x

we would need to assume percentages for either or x or y and solve for the other quantity.
Example:
So if we are ahead 60% (x) of the time he needs to 3-bet us with a worse hand 5% (y) of the time for the c/r to be equal to c/c.

Here is a chart of how this breaks down:
<font class="small">Code:</font><hr /><pre>
x y x+y
0.5 0.125 0.625
0.51 0.1175 0.6275
0.52 0.11 0.63
0.53 0.1025 0.6325
0.54 0.095 0.635
0.55 0.0875 0.6375
0.56 0.08 0.64
0.57 0.0725 0.6425
0.58 0.065 0.645
0.59 0.0575 0.6475
0.6 0.05 0.65
0.61 0.0425 0.6525
0.62 0.035 0.655
0.63 0.0275 0.6575
0.64 0.02 0.66
0.65 0.0125 0.6625
0.66 0.005 0.665
</pre><hr />

edit:
this really makes me want to c/c instead of c/r (I was never in favor of c/r'ing).

It is a little harder to add an analysis of betting out and calling a raise compared to simply checking.

[cartman]

[ QUOTE ]

Where is Cartman when I need him?!

[/ QUOTE ]

Like any poker situation, the most thorough way to analyze this is with a comprehensive tree diagram, which sometimes gets big enough to cover a football field. You can usually short-circuit the process with assumptions. Obviously the more of them you make and/or the broader you make them, the less accurate your conclusion will be.

In this situation, your first set of branches would only have two choices: CHECK and BET. When your diagram is complete you just pick the branch with the higher EV and do it. Lets say in this case that you find out that the CHECK branch has the higher EV so you do it and he bets. Now you find in your diagram that exact path (first branch CHECK, second branch HE BETS). There will be 3 branches coming out from that spot: RAISE, CALL, and FOLD. Again you pick branch with the highest EV and do it. You use the same process for determining whether to call if you CR and he 3 bets.

In this particular case, I would use a simpler approach than the full analysis I described above. For example, lets assume that we check and he bets, and we are trying to determine whether to raise or to call. We will always call if he 3-bets. Here are the parameters we need:

1) how often does he have a better hand
2) given that he has a better hand, how often does he
a) 3-bet
b) call
c) fold
3) given that he has a worse hand, how often does he
a) 3-bet
b) call
c) fold


Now since if we just called his bet, we would always lose 1BB when he had a better hand and win 1BB when he had a worse hand, I would look at the analysis of the CR decision relative to the call. For example, find the probability he both has a better hand and 3-bets and multiply it by -2, because we will be 2BB worse off than if we had just called. Then find the probability that he both has a better hand and just calls and multiply it by -1, because we will be 1BB worse off than if we had just called. Etc. Find each of these probabilities and multiply it by its relative result to checking and calling and then add up the terms. If the sum is positive then you conclude that, given that we check and he bets, raising is better than calling.

Sorry to be vague, I'm in somewhat of a hurry.

Cartman