Perfect example from SSHE that I botched.

[kiemo]

Fold preflop.

You really think a player who plays 15% of their hands is raising lightly UTG.

[00Snitch]

[ QUOTE ]
Put villain on a hand range. How often does villain hold a pair and how often does he have two high cards? How often does the flop come down as a "non-high-card flop"? How often does villain's high card catch you on the turn? (Presumably, he's not folding on the flop if it's all undercards.) When the flop comes as a "non-high-card flop", are you able to get away from your pair of 9s if villain keeps attacking (say you have a 853 flop or a J76 flop)?

[/ QUOTE ]

handt done something like this in a while, so i thought i would give it a crack.

i havnt really looked at the hand, so i dont know how these numbers apply. just wanted to see if i could get it right [img]/images/graemlins/tongue.gif[/img]

please correct where wrong.

Hands
----------------
AA - 12
KK - 12
QQ - 12
JJ - 12
TT - 12
AK - 16
AQ - 16
AJ - 16
KQ - 16

16*4 = 64
5*12 = 60
total= 124

48.3% Pair
51.7% High cards

-----------

Flop is all high cards (A,K,Q,J,T)
20/50 * 19/49 * 18/48
= 20*19*18/50*49*48
= 6840/117600
= 5.8%

-------------------

At least 1 high card

20/50 + 20/49 + 20/48
= 20*49/50*49 + 20*50/49*50 + 20/48
= 980/2450 + 1000/2450 + 20/48
= 1980/2450 + 20/48
= 1980*20/2450*48 + 20*2450/48*2450
= 39600/117600 + 49000/117600
= 88600/117600
= 75.3%

--------------------

Pairing either on flop

6/50 + 6/49 + 6/48
(6*49/50*49 + 6*50/49*50) + 6/48
= 294/2450 + 300/2450 + 6/48
= 594/2450 + 6/48
= 594*48/2450*48 + 6*2450/48*2450
= 28512/117600 + 14700/117600
= 43212/117600
= 36.7%

------------

Pairing either on flop or turn

43212/117600 + 6/47
= 43212*47/117600*47 + 6*117600/117600*47
= 2030964/5527200 + 705600/5527200
= 2736564/5527200
= 49.5%

[Xhad]

[ QUOTE ]
In order of importance, (imo)
1. become the aggressor

[/ QUOTE ]

Why would you want to be the aggressor here? This is an argument against 3betting preflop!

I fold preflop, but if I'm playing I'm coldcalling planning to raise favorable flops. The flop play is excellent but I hate the turn bet; there are a variety of reasons for UTG's cap and check but most of them involve us being crushed, except when s/he has A [img]/images/graemlins/diamond.gif[/img] K.

[Bruce D]

Well lets analyse it like this.

We will say that we are NEVER good on the river. However, that is only because we are behind to UTG 100% of the time. UTG is weak tight. UTG will never fold for one bet because the pot is so big. But let us summise that she will fold for 2 bets 40% of the time. The other 60% she calls and takes the pot. When she folds let us say that I beat UTG1 85% of the time (Only a jack or a Q beats me and he doesn't have a PP higher than 7 and he never has the flush) and he will call one more 40% of that and MHIG.

How can we put this into a formula that shows the expected value?

[00Snitch]

wouldnt that just be 0.4(0.85*15.25) - 0.6(2) = 3.98

that seems too simple. am i doing somethig really wrong there?

how about when you get 3-bet by UTG+1 or when UTG does infact call 2.

[Hielko]

That's easy: you are going to win (assuming that your numbers are right) the pot 0,4*0,85 = 0,34% of the time. 0,34 * 14,24BB (assuming both players fold) = 4,845 BB. Now we need to subtract the 2BB the river raise is going to cost us in the 0,66 of the times that we loose the pot: 1,32 BB.

We win on average 4,845 BB, we loose on average 1,32 BB so this results in an ev of 3,525BB.

So when your assumptions are correct raising the river is way better than calling.

That said; I think your assumptions are wrong! The probability that you win rfom UTG+1 is really a lot lower than 85%, just a small (incomplete proof):

[ QUOTE ]
Board: 8d 8c 3d Jd Qc
Dead:

equity (%) win (%) tie (%)
Hand 1: 61.4646 % 61.41% 00.05% { 9c9d }
Hand 2: 38.5354 % 38.48% 00.05% { random }


[/ QUOTE ]

Since UTG is going to have something better than random cards, the probability that your hand is best is in fact a lot lower.

When we assume that you will beat UTG+1 40% of the time and that UTG will in fact just fold 25% of the time the EV of a river raise is:

0,25 * 0,4 = 0,1

You will win 14,25 * 0,1 == 1,425 BB on average
You will lose 2 * 0,9 == 1,8 BB on average

Using these assumptions the river raise has an EV of -0,375 on average.

Note that this still implies that raising the river >> calling the river, but as already posted: I check the turn and fold the river UI.

[Hielko]

[ QUOTE ]
wouldnt that just be 0.4(0.85*15.25) - 0.6(2) = 3.98

that seems too simple. am i doing somethig really wrong there?

how about when you get 3-bet by UTG+1 or when UTG does infact call 2.

[/ QUOTE ]
It's almost right, but your calculations miss the fact that you also lose two BB when UTG folds but UTG+1 has a better hand.

[00Snitch]

hielko, im being a nit, but shouldnt that be 0.34 * 15.25 because we have decided that UTG+1 will call the last bet if we raise?

[Bruce D]

I think we have to add the money that goes in when UTG1 calls and he is behind in there. Is the money I lose 15% of the time when UTG1 has a J or Q in there somewhere?

If UTG doesn't fold, I ALMOST never win. I either muck, or fold to a 3bet. She has QQ, KK, or AA here almost always. The only way I win is if she over played AK.

[00Snitch]

[ QUOTE ]
It's almost right, but your calculations miss the fact that you also lose two BB when UTG folds but UTG+1 has a better hand

[/ QUOTE ]

ok, now im confused...

my formula says:

40% of the time we win 85% of a 15.25 bb pot. this is when UTG folds and 85% of the time we beat UTG+1.

60% of the time, we throw away 2bb.

isnt that what you have written (apart from the fact i have called the pot 15.25BB rather than 14.25)?