Baby flush vs. slowplayer

[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.

[MarkD]

[ QUOTE ]
[ QUOTE ]
"Are we ahead &gt;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.

[milesdyson]

[ QUOTE ]
i cant imagine why we wouldnt cr here.

[/ QUOTE ]
Yeah this one is "easy" IMO.

[Grisgra]

[ QUOTE ]
. . . 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.

[/ QUOTE ]

On this board, in this situation I can't imagine a case where we bet a hand that our opponent will call with (or raise with), but will check behind if we check. And betting stops him from continuing to bluff with his KJ or 54 UI.

On this board, I think I agree that we probably aren't ahead 67% of the time, but it's close given OP thinks the villain might play AA or KK or AQ this way. Give us some higher hearts, unpair the board, even make the '3' something higher, and I think we're there (well, certainly if we unpair the board.) It's a useful comparison number, though probably 64-65%, given the chance of an overplaying river 3-bet, is better.

[MarkD]

Sorry, I was thinking about the KQ hand when I wrote everything in my above posts. The math is the same in either case though - you just plug in percentages.

edit:
I would c/r this hand all day and only be afraid that my opponent might check behind. This was my thought before doing any math. Now that I have done the math I'd still CR as I would estimate I'm ahead much more than 2/3 times.

I just wanted to investigate the math behind the "60% rule" that grisga kept bringing up. The above formulas give a means of evaluating c/r'ing vs. c/c'ing in any river situation though so it wasn't a wasted effort on my part.

[milesdyson]

[ QUOTE ]
[ QUOTE ]
. . . 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.

[/ QUOTE ]

On this board, in this situation I can't imagine a case where we bet a hand that our opponent will call with (or raise with), but will check behind if we check. And betting stops him from continuing to bluff with his KJ or 54 UI.

On this board, I think I agree that we probably aren't ahead 67% of the time, but it's close given OP thinks the villain might play AA or KK or AQ this way. Give us some higher hearts, unpair the board, even make the '3' something higher, and I think we're there (well, certainly if we unpair the board.) It's a useful comparison number, though probably 64-65%, given the chance of an overplaying river 3-bet, is better.

[/ QUOTE ]
How could we not be good 67% of the time? I'd guess more like 80%.

[Grisgra]

[ QUOTE ]
How could we not be good 67% of the time? I'd guess more like 80%.

[/ QUOTE ]

I dunno, the read the OP seemed to have on villain was that he slowplays monsters, meaning that I figured villain would *usually* bet the flop with boring old top pair.

[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