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PL/NL Texas Hold'em >> Small Stakes

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fimbulwinter
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Calculating EV Part II: Making an All-In Raise
      #3069765 - 08/06/05 09:18 AM

Previously, in this thread, I went over the easier EV calculations that go on when facing an all-in bet. This post will deal with (in much shorter order) the math behind making big all-in "bluffs" with drawing hands. These can be very profitable plays, but they are very easy to do poorly.

This post will assume you've read the previous one. If you haven't, then go read it first, then read this one. Although it is shorter, it is also more complex and will probably be hard to read if you don't read the other one first.

Here's a general framework on how to think about this: in general when we were discussing calling, we were getting odds like 2:1 on our draw. now that we're betting and raising, we'll be doing thing things like betting 4 to win 2 etc. Since we often have hands with less pot equity than that (50%, 35% etc) these plays are almost never profitable if the opponent will call every time. Thankfully this is not the case.

Part II: Calculating EV of All-In Semibluffs

First let's look at the PSR (pot sized raise). this is generally more than we will raise most often (if the pot is 100 and he bets 100 then a PSR is a raise to 400), but it makes the math easier. then we'll go back and look at smaller raises (like say 3/4 or 2/3 pot) like those we typically make.

A PSR has us betting 4 to win 2 (we offer our opponents 2:1 on their call. if our all-in is roughly a PSR (say moving 200 into a PSB of 50) then we can use the equities of various draws to calculate folding equity we need to make them neutral EV.

1/3 equity draw (standard flush draw vs TPTK/overpair)
EV = 2x + (1-x)((1/3)(10)-4)
EV = 2x + (1-x)(-2/3) [you can think of -2/3 as the long term "cost" we pay every time we get called]
0 = 2x + 2/3x -2/3
2/3 = 8/3x
x = 2/8 = 25% of the time they must fold in order for this to be profitable.

@ a more standard 2/3PSR (pot = 1, his bet = 1, your raise = 3)

EV = 2x + (1-x)((1/3)(8)-3)
EV = 2x + (1-x)(-1/3) [our "cost" is now half the above, though our raise is 3/4 the size of the above raise]
0 = 2x + 1/3x - 1/3
1/3 = 7/3x
1/7th of the time he needs to fold to make the raise profitable

this result is encouraging (we don't need a fold even half the time) however, looking at the equation, there is room for improvement. since we really cannot change the raise size (say making a smaller or larger all-in raise) we instead look to increase our pot equity on this move by picking stronger draws with which to do it.

Notice something interesting: once we set our pot equity at 40%, our all-in PSR is a freeroll. namely, if we had an exactly 40.01% draw, we should call an all-in PSR, so making one ourselve just lines our pockets with free sklanskybucks every time we get someone to fold.

Now, onto the hands:



Ex1: Simple

you end up in a raised pot of 20BB on the button with a flush draw on a raggy flop and maybe clean overcard worth ~1 out. your opponents cover you and you have 100BB in your stack.

opponent 1 bets pot, opponent 2 calls.

assuming opponent 2 will always fold if opponent 1 does (as opponent 2 is smart enough to raise his monsters on drawing boards), and that if called, only one will call, how often must they fold?

well, here we're making a PSR (60BB in pot, 20 to you, PSR = your stack) with ~4*10 = 40% equity.

EV = 60x + (1-x)((.4)(240) - 100)
EV = 60x + 4x - 4 [the "cost" of getting caught here is a mere 4BB...]
x = 4/64 = 6.25% they must fold.


Ex2: Intermediate

My buddy, we'll call him L, wishes to not be outplayed by DW on his right, and so he wants general neutrality in his bet/3bets ST DW cannot make the right decision against him.

assuming L will always have ~10 outs on his draws and will always be facing 2/3 PSR's from DW and will always have another PSR to that PSR in his stack for the 3bet, how often should he be doing this with a set vs draw in order to make DW's calling EV neutral?

assume the pot is 10, we'll bet 10 and get raised to 30, when we'll shove 100 total in over the top. DW will be facing 70 more to play a 210 pot or getting 2:1 on his call.

DW sees it like this:

need 1/3 pot equity to make the call. when he has draw, have 60% PE. when he has set, have 5% PE.

.33 = .05x + (1-x).6
.27 = .55x
x = 49% of the time he should have a set when he bet/3bets to make DW unable to play profitably without reads

Ex3: Advanced

Our hero, from time to time, really likes to speed. on certain turns that a pro player would feel scared getting raised on (say 89 on 4587r) he will do things like put in big raises with a pair and a gutshot because he feels his fold equity is so good. when he does this, he has 9 outs (3 twopair, 2trips and 4 gutshot) and makes PSR's. how much folding equity needed?

EV = 2x + (1-x)((1/5)(10) - 4)
EV = 2x + 2x - 2
x = 50%


Problems:

All these are hands against DW, so you can assume the player is smart.

1. L has 99 and leads into DW on a board of J96 with two clubs, DW raises and L pushes. I say ni han. why?

2. L has JT and leads into DW on a board of Q93r, DW raises, L moves in for a 2x PSR. I say ni han. why?

3. A LP player makes a CB after a PFR. board QT8 w flush draw. DW has 96 with the flush draw and C/R PSB the flop which takes 1/4 of his chips (he is covered). I don't like it. why?


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BearHustler
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3069793 - 08/06/05 09:34 AM

Yes! Part two!

Now I'm gonna read it

Edit after reading:

Wow. Great work fim. I understand what you're saying, but I feel I'm such a long way from being able to apply this in concrete situations.

One of your best so far. I hope you keep 'em coming. Thanks for posting this stuff.

Edited by BearHustler (08/06/05 10:03 AM)


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BearHustler
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3069808 - 08/06/05 09:45 AM

I think this line: EV = 2x + (1-x)((1/3)(10)-4)

Should be something like this:

EV = 2x + (1-x){(1/3 * 6) + (2/3 * (-4))}
=> EV = 2x + (1-x)(6/3 - 8/3)
=> EV = 2x + (1-x) * (-2/3)

Edit: your way of calculating gives the same result, but I don't understand what 1/3 * 10 - 4 means

I thought it would be something like: 1/3 of the time you draw out and win 6 , 2/3 you don't and lose 4, hence the formula I wrote down.

So the results are the same, I just don't understand the way you calculate it...

Edit 2: for the people who missed your poll, you forgot to mention that DW = David Williams.

Edited by BearHustler (08/06/05 10:01 AM)


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fimbulwinter
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Re: Calculating EV Part II: Making an All-In Raise [Re: BearHustler]
      #3072006 - 08/06/05 05:46 PM

Quote:

I think this line: EV = 2x + (1-x)((1/3)(10)-4)

Should be something like this:

EV = 2x + (1-x){(1/3 * 6) + (2/3 * (-4))}
=> EV = 2x + (1-x)(6/3 - 8/3)
=> EV = 2x + (1-x) * (-2/3)

Edit: your way of calculating gives the same result, but I don't understand what 1/3 * 10 - 4 means

I thought it would be something like: 1/3 of the time you draw out and win 6 , 2/3 you don't and lose 4, hence the formula I wrote down.

So the results are the same, I just don't understand the way you calculate it...

Edit 2: for the people who missed your poll, you forgot to mention that DW = David Williams.




oops, yes, DW is indeed david williams.

as for the math: each time we make this move, it costs us 4 (-4) and we "get" 1/3 of the final pot size.

fim


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WoolyHat
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3072056 - 08/06/05 05:53 PM

Nice post, fim. Thanks for taking the effort to write this.

I've spent a lot of time working on the maths of fold equity, myself. If I'd seen a post like this before I'd started, it would have saved me a lot of time. I just hope others appreciate how good this is.

I'm suprised you haven't received a larger repsonse...


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fimbulwinter
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Re: Calculating EV Part II: Making an All-In Raise [Re: WoolyHat]
      #3072174 - 08/06/05 06:13 PM

Quote:


I'm suprised you haven't received a larger repsonse...




You forget that to most players posts like this look like the ramblings of a madman.

fim


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crosse91
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3072300 - 08/06/05 06:33 PM

i'm moving today so i just skimmed the hands part-and i don't like hand 3 b/c your stuck with a large potsize on the turn if you miss and are oop. Making things very hard and you could get reraised and have another tough descision to make. Potsize would then be about your stack correct? Plus, if you hit you might not get paid off.

God, i'm simple and blind to the mathmatics behind this game.


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dtbog
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3072974 - 08/06/05 08:30 PM

Quote:

You forget that to most players posts like this look like the ramblings of a madman.




AAAAAIIIIIEEEEEEEEE!


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dtbog
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3073004 - 08/06/05 08:33 PM

The one thing I would add to this discussion is that amid all of these calculations, we sometimes forget why we're actually making these plays -- and it's not just about folding equity or putting yourself in a good position to win the current hand.

Shania, shania, shania! Think about what your opponents think of you!

Think of how many times you sit at a table with a "maniac" or "fish", who you classified as such because he keeps putting all of his chips in the middle. People call his big bets a lot, don't they?

If you're at a table of players who are good enough to notice what's going on at the table, but not good enough to analyze it properly ($100 and $200 NL are prime examples IMO), then plays such as the one that fim describes will buy you future action to a great degree.

For a little obvious example, take a standard $200NL full ring table with average opponents. You twice flop a flush draw with overcards and call your opponents' underbets on the flop and turn. When you miss, you autofold the river.

Now you flop a set on a drawing board. EP leads out, MP calls... and you push. They know you don't push your draws, so they know you have a set. They fold.

If you've raised/pushed your good draws in the past, they'll have a lot of reasons to look you up here. If you didn't show down your semi-bluffs before, they might think you're just a bully. If you did, they'll put you on a very wide hand range, and talk themselves into calling with TPTK drawing nearly dead. By making plays like this, you make yourself very hard to play against.

This is important.


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ChipWrecked
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3074269 - 08/07/05 12:36 AM

Thanks fim. I'd been looking forward to this. Well done sir.

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-Skeme-
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3074595 - 08/07/05 01:34 AM

I don't understand any of this.

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Allinlife
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Re: Calculating EV Part II: Making an All-In Raise [Re: -Skeme-]
      #3074675 - 08/07/05 01:51 AM

EV?


j/k nice post fim..now I can dig up some hands on PT and check out the FE %' i've always wanted to work on...tomorrow


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Malachii
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Re: Calculating EV Part II: Making an All-In Raise [Re: -Skeme-]
      #3075021 - 08/07/05 03:14 AM

Quote:

I don't understand any of this.


I've been working on getting better at applying the math in situations like this... I really think if I want to take my game to the next level, I have to have a really good fundamental understanding of the odds and how often plays such as this need to work.

On a side note, I made a post in the probability forum about a week ago that I found reasonably helpful with understanding the math... you can check it out here


PS: Excellent post Fibmul, as usual.


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-Skeme-
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Re: Calculating EV Part II: Making an All-In Raise [Re: Malachii]
      #3075209 - 08/07/05 03:51 AM

I just don't understand the equations and such. Can't read them. My math is beyond horrendous.

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fimbulwinter
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Re: Calculating EV Part II: Making an All-In Raise [Re: -Skeme-]
      #3075821 - 08/07/05 08:20 AM

Quote:

I just don't understand the equations and such. Can't read them. My math is beyond horrendous.




skeme-

from having read your posts, i know this is not beyond you.

read the shorthand problems in both of the posts (advanced on each). you don't need to be crunching decimals to incorporate this- learning the mental shorthand is definitely +EV.

fim


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crosse91
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3076076 - 08/07/05 10:45 AM

there's a good post in the prob. forum where this is explained, i'll have to find it though-give me awhile i'm moving out of my house.

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BirdieLongSocks
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3076084 - 08/07/05 10:49 AM

Your an ace in my book fim !

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RiverFenix
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Re: Calculating EV Part II: Making an All-In Raise [Re: BirdieLongSocks]
      #3076141 - 08/07/05 11:07 AM

If Fim ever stops posting on SSNL it will be a sad day

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punter11235
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3076184 - 08/07/05 11:18 AM

Nice post Fimbul.
Its good you are propagating mathematical awareness here.


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GoCubsGo
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3076464 - 08/07/05 12:23 PM

Nice post. Had to read it a couple times before I understood it, but now that I do, I'm surprised by the results. This will be a great play to incorporate into my game. Not only is it profitable, but for the times you do get called, it is great advertising that you're a maniac.

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theblitz
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3076948 - 08/07/05 01:53 PM

Still can't figure out where the
Quote:

EV = 2x + (1-x)((1/3)(10)-4)



part comes from.
Bear's version seems to be right but the result is the same.
Can you please explain how your one works?


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theblitz
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3078229 - 08/07/05 05:01 PM

Can someone please explain where the formula:

EV = 60x + (1-x)((.4)(240) - 100)

comes from?

The maths is NOT a problem with me. I just don't see where the 240 comes from.


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-Skeme-
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3078577 - 08/07/05 05:42 PM

I have the math skills of a 5th grader.

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Malachii
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Re: Calculating EV Part II: Making an All-In Raise [Re: -Skeme-]
      #3078583 - 08/07/05 05:44 PM

Quote:

I have the math skills of a 5th grader.




Doesn't mean you can't get better.


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-Skeme-
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Re: Calculating EV Part II: Making an All-In Raise [Re: Malachii]
      #3078598 - 08/07/05 05:45 PM

True, just saying these are way over my head at the moment. I've bookmarked the page, though.

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GoCubsGo
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Re: Calculating EV Part II: Making an All-In Raise [Re: theblitz]
      #3078885 - 08/07/05 06:27 PM

Quote:

Can someone please explain where the formula:

EV = 60x + (1-x)((.4)(240) - 100)

comes from?

The maths is NOT a problem with me. I just don't see where the 240 comes from.




The total pot will have 240 in it if your opponent calls.


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theblitz
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Re: Calculating EV Part II: Making an All-In Raise [Re: GoCubsGo]
      #3079352 - 08/07/05 07:28 PM

Thx.
But I must be brain-dead today cos I still can't figure how we get from

EV = 60x + (1-x)((.4)(240) - 100)

To

EV = 60x + 4x - 4

I seem to be missing a factor of 10.

It IS 2:30 a.m. - so that could be part of the problem.


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GoCubsGo
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Re: Calculating EV Part II: Making an All-In Raise [Re: theblitz]
      #3080075 - 08/07/05 09:15 PM

Quote:

Thx.
But I must be brain-dead today cos I still can't figure how we get from

EV = 60x + (1-x)((.4)(240) - 100)

To

EV = 60x + 4x - 4

I seem to be missing a factor of 10.

It IS 2:30 a.m. - so that could be part of the problem.




60x + (1-x)((.4)(240)-100)
.4(240) = 96

60x + (1-x) (96-100)
96-100 = -4

60x + (1-x)(-4)
(1)(-4)= -4
-x(-4) = 4x

60x + 4x -4

It's okay my math sucks at 2:30 also.


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foldem
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3080865 - 08/07/05 11:06 PM

Nice post. I remember the first time I calculated the EV of a semibluff raise I was very surprised with how small the percentage of the time the villain needed to fold in order to make the play +EV.

What is your plan if you lead out on the flop with a draw and are cold called instead of raised?

I assume you don't like the C'R in problem three because hero is out of position in a big pot on the turn with potentially nothing but a draw.


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theblitz
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Re: Calculating EV Part II: Making an All-In Raise [Re: GoCubsGo]
      #3082830 - 08/08/05 04:03 AM

Quote:

Quote:

Thx.
But I must be brain-dead today cos I still can't figure how we get from

EV = 60x + (1-x)((.4)(240) - 100)

To

EV = 60x + 4x - 4

I seem to be missing a factor of 10.

It IS 2:30 a.m. - so that could be part of the problem.




60x + (1-x)((.4)(240)-100)
.4(240) = 96

60x + (1-x) (96-100)
96-100 = -4

60x + (1-x)(-4)
(1)(-4)= -4
-x(-4) = 4x

60x + 4x -4

It's okay my math sucks at 2:30 also.



Just shows what a little sleep can do.

I had (0.4)(240) coming out at 60.


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theblitz
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #3135437 - 08/13/05 04:33 PM

Quote:

1. L has 99 and leads into DW on a board of J96 with two clubs, DW raises and L pushes. I say ni han. why?

2. L has JT and leads into DW on a board of Q93r, DW raises, L moves in for a 2x PSR. I say ni han. why?

3. A LP player makes a CB after a PFR. board QT8 w flush draw. DW has 96 with the flush draw and C/R PSB the flop which takes 1/4 of his chips (he is covered). I don't like it. why?




Now that we mere mortals have had a chance to study this (amazing) post - could you give us the answers to these 3 questions?


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fimbulwinter
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Answers to the questions [Re: fimbulwinter]
      #3136876 - 08/13/05 09:09 PM

almost forgot here.

NOTE: as previously stated, i forgot to say that DW = David Williams. So we're dealing with someone who can think here.

1. This board is massively draw heavy. basically any two reasonable clubs here could flop OESFD, Pair+GS+FD etc. therefore when someone plays fast at you on this kind of board it's more likely to be a draw than on a K72r board. (NOTE: THIS STILL DOES NOT MEAN YOU SHOULD GET YOUR CHIPS IN WITH KK ETC. SEE PART I FOR WHAT IM TALKING ABOUT)

DW knows this and so the folding equity of bet/threebet is very low, the likelyhood of a raise is very high and there are a ton of turn cards that kill hero's action, so, well played.

2. This board is pretty dry. bet/3bet with JT is good because he has a good likelyhood of taking it down unless someone has a Q with the initial bet. when raised, it is really hard for DW to call with one pair knowing that, on this board, he's very likely to be show a set. therefore, though the draw is not one of our 40-50% monster draws, it more than makes up for it by having such great fold equity against DW given the board.

3. tons of reasons here. everyone knows this creates a terrible turn situation, but one you might not have considered is the risk/reward ratio. basically, he created a small pot and risked his whole chipstack to win it (he gets pushed on here by set/twopair and wins a small pot from weak onepair hands.) so while he may have been initially "risking" say, 140 to win 100 with the C/R, he actually was risking much more.

fim


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Guy de France
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Reged: 02/23/06
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #4841544 - 02/23/06 04:02 AM

Hello,

I have read this interesting post, but I don't understand why the final pot size is 10.

Pot = 1
Opponent1 raises 1 => Pot = 2
I raise 4 => Pot = 6
Opponent1 calls to 4 (+3) => Pot = 9

So EV = 2x +(1-x)((1/3)9 - 4) = 3x - 1
and x = 1/3

What'is wrong with me?

Thanks a lot


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kazana
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Re: Calculating EV Part II: Making an All-In Raise [Re: fimbulwinter]
      #5704260 - 05/05/06 11:22 AM

Quote:

@ a more standard 2/3PSR (pot = 1, his bet = 1, your raise = 3)

EV = 2x + (1-x)((1/3)(8)-3)




I'm not sure if I'm just plain blind or stupid, but counting what is in the pot after getting our 2/3PSR called I get this:
initial pot: 1
bet by him: 1
my raise: 3
his call: 2 (and not 3, he already has 1 in from betting)
================
total: 7

The same goes for the example above this one, there should be only 9 in the pot and not 10.
And for the unlikely event that I'm not wrong, we need our buddy to fold 33.33%+ for the PSR and 25%+ for the 2/3PSR to be profitable.

Someone tell me I'm wrong, please.


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ilya
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Re: Calculating EV Part II: Making an All-In Raise [Re: Guy de France]
      #6979954 - 08/19/06 11:10 AM

I think you're right, Guy, I think fimbul made a mistake in the math. The fold% in that first example to break even should be 33%, not 25%.

Edited by ilya (08/19/06 11:11 AM)


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