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bigspenda73
Old 01-05-2007, 11:43 AM     Post subject: Help a math Noob out #1 (permalink)  
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 Having problems calculating crap. I have all this theory running through my brain but I feel like I do not have the tools to work it out on paper. Here's a typical thought I am struggling with.

Assume typical limit game with 1/2 blind structure and sane opponents.

All folds to Hero who opens OTB. BB calls with whatever

Flop(4.5Sbs): :Jh:

BB donks and hero calls

Turn(3.25BBs):

BB donks again, Hero?

Here is what I am having trouble with calculating. It's the EV in raising/calling here. My theory first. There are two possible outcomes that could happen from raising. Villian calls/3bets. There is obv one outcome that could happen from hero calling. If villian 3bets he will always bet the river. If villian calls he will c/c the river. Here, we're assuming BB has defended with Ax.

I want to calculate the EV in raising (getting either called/3bet) and the EV in calling. How do I do this? Do I include the pot in either of the calculations or is it strictly the action from the turn on. Also, in a perfect world we would fold the river knowing what we know. However, we obv do not have this information. Would it look anything like this?

If villian calls the raise and will check the river (we will check behind)
(-.68)*7.25+(.32)*9.25

If villian 3bets and will lead/call the river. We will fold to a lead UI and raise a lead with either a flush/2pr/trips
(-.68)*9.25 + (.32)*13.25

Then we would have to determine the percentage of times villian would 3bet us and how many times he would c/c. Let's just say he 3bets only 10% of the time.

ARGHH, looking over it again I know this cannot be right. The calculations should not take the pot into account right? Someone help. Also, please just don't show me the equation, I really need a well worded explanation.

Thanks guys.
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swiggidy
Old 01-05-2007, 01:18 PM #2 (permalink)  
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 Not sure what your numbers are but I'll take a stab.
(-.68)*7.25+(.32)*9.25

my assumption:
.68 chance hero misses
.32 chance hero hits and wins

first part should be
-.68 * 2

where 2 is the number of bets remaining for you to put into the pot because this is what you will loose (don't include pot here because it's not yours and you don't loose it)

the second half is
.32 * 9.25

where 9.25 should be the size of the pot plus the extra bets you expect to win from villain

this is the eV from a call (say ceV), you should be able to do the math for the raise (reV)

now if 0.10 is how often he raises, your overall eV is
0.1 * reV + (1 - 0.1) * ceV

If you really want the whole formula build for you I guess I could. My head hurts from doing maths this morning already and it would be better for you to do it yourself, especially since you're so interested.
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sinky
Old 01-05-2007, 01:20 PM #3 (permalink)  
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OK, first thing about EV is that you only consider bets from this point forward. The money in the pot has no bearing on EV. but lets take a step back...

First you have to estimate your chances of winning this hand. Lets say you have a good read and have correctly assumed you are behind to Ax. So you have 9 outs for a flush, 3 Kings for 2 pair and 2 Jacks for trips. Total 14 outs. On the river you are 14/46 which is aprox 3.3 :1 odds (30%)

The first decision you have to make is whether to fold or continue. This is done by comparing the pot odds (4.25:1) against your chances of winning. In this case, easy decision, as you are getting a minimum of 4.25 :1 pot odds against your 3.3:1 odds to win the hand.

Once you have decided to continue you have to determine if you should raise or just call. This is where the EV calculation comes in...

Scenario 1. You call turn and if you miss will check behind or fold and if you hit opponent will check call. ie) 30% you will win 2 bets, 70% you will lose 1

(0.3 * 2) + (0.7*-1) = -0.1EV

Scenario 2. you raise the turn. Lets say 50% of the time you will be 3bet and 50% of the time you are called, so the turn will cost on average 2.5BB. Either way if you hit you will get 1 more BB on the river.

(0.3*3.5) + (0.7*-2.5) = -0.7EV

Even if you are sure you can get 2BB out of him on the river every time the EV is still negative.

(0.3*4.5BB)+(0.7*-0.25) = -0.4EV


Obviously you don't have time to do all these calculations at the table. But here is a simple way to look at it. You are Heads up on the turn, from this point forward you will contribute 50% of all future bets to the pot. So if your odds to win are > 50% then you have an equity edge and a raise will usually be better than a call. In this case you are only 30% to win so a raise is bad. Similarly against 2 opponents you need to have > 33% chance of winning to make raising +EV.
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swiggidy
Old 01-05-2007, 01:28 PM #4 (permalink)  
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 ^^ don't forget the 3BB already in the pot, that will drastically swing your maths

(0.3 * (2 + 3) + (0.7*-1) = +0.8 EV
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sinky
Old 01-05-2007, 01:47 PM #5 (permalink)  
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Quote:
Originally Posted by swiggidy
^^ don't forget the 3BB already in the pot, that will drastically swing your maths

(0.3 * (2 + 3) + (0.7*-1) = +0.8 EV
When calculating EV you do not include money already in the pot. The EV of any decision relates to what you expect to happen next. Not what has gone before.

Like I said before....
Pot size determines fold / continue.
EV determines raise / call.
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swiggidy
Old 01-05-2007, 02:34 PM #6 (permalink)  
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 No, eV describes your expected return on an action

You say you need 4:1 odds to call for a flush correct? That means there are 4 bets in the pot already.

Suppose there are 5 bets in the pot. What if opponent folds every time when a flush card hits?

By your reasoning
.2 * 0 + .8 * -1 = -0.8 eV

By my reasoning
.2 * 5 + .8 * -1 = 0.2 eV

So is calling a 1:5 payout with 4:1 odds slightly +eV or largely -eV?

Quote:
Like I said before....
Pot size determines fold / continue.
EV determines raise / call.
folding is 0 eV because it costs nothing you lose nothing. The pot size helps determine weather calling and/or raising is better than folding (and which is better relative to each other). Pot size is a subset of eV, they are not independent.

if cEv and rEv < 0 you "gain" by folding because you lose the least, even though you don't actually gain anything
if cEv and rEv > 0 you "lose" by folding because you win the least, even though you don't actually lose anything

This is an extremely basic concept.

{Edit: lol, fixed. I if ever remember which is which it'll be because of this thread}
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Old 01-05-2007, 06:11 PM #7 (permalink)  
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from dictionary.com

Quote:
loose:
free from anything that binds or restrains; unfettered
Quote:
lose:
to fail to keep, preserve, or maintain
OT, but this is a pet peeve of mine.

on topic, uh...what swiggidy said.
 
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Xanadu
Old 01-05-2007, 09:03 PM #8 (permalink)  
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Yeah, it always annoys me as well when people confuse loose and lose.

Nice to see you back at the limit forums Hyper.

P.S. I refrained from doing any math and answering the question because I hate doing the math when the answer is painfully obvious for the particular example. I think you answered your own question on the correct play, spenda, when you said to assume villain has Ax. Raising cannot be right on the turn because no reasonable player folds TP just because someone raised the turn, and if your read of Ax is correct the raise is not for value because your winning chances are less than 50%. No fold equity, no value, no bet.
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bigspenda73
Old 01-05-2007, 09:34 PM #9 (permalink)  
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 Yea, I realize it has to be -EV when we are behind and villian is ahead. We obviously do not win the pot enough times to warrant putting in more bets on the turn than need be. However, the real question behind this is about "free" or "cheap" showdowns. I probably fouled the concept up by stating that we know the BB defended with Ax. Im having a bit of troubling determining a situation where we would want a free showdown and could possibly be ahead but could possilby be behind. Say 2/3 of the time he has Ax but 1/3 of the time he has Jx. What is our value in raising and seeing a free river card. I would guess it would have to be +EV from the turn on as we will still only lose 2 bets to a better hand but will obv gain more bets when we hit our hand.
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Xanadu
Old 01-05-2007, 10:50 PM #10 (permalink)  
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The free showdown play is generally not a raise on the turn. It is more typically betting with position with an under-pair to the board (say you have TT and the board is K742), or you have a good A-high hand and suspect your opponent has nothing. The free showdown play is not a good idea as a raise on the turn because most players do not bet thet turn without some kind of hand. This is a tool for getting some money when ahead and having a chance to showdown cheap when behind with a somewhat to very marginal hand. Why would you raise the turn for free showdown when just calling both turn and river would cost the same?
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bigspenda73
Old 01-05-2007, 11:51 PM #11 (permalink)  
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 Because you can put in another bet when you know you're ahead.

I.E.- you showdown for the same when you're behind and you win 1BB more when you improve.
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Xanadu
Old 01-06-2007, 12:17 AM #12 (permalink)  
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Quote:
Originally Posted by bigspenda73
Because you can put in another bet when you know you're ahead.

I.E.- you showdown for the same when you're behind and you win 1BB more when you improve.
Um, but you're putting the extra bet in on the turn trying for a free showdown when you don't know you are ahead ... risking having to pay 3 or 4 bets to showdown rather than 2.

That's my whole point. Take the turn cheap, then put the extra bet in on the river if you hit.

You don't showdown for the same when behind unless you are lucky.
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sinky
Old 01-08-2007, 12:36 PM #13 (permalink)  
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Quote:
Originally Posted by swiggidy
No, eV describes your expected return on an action

You say you need 4:1 odds to call for a flush correct? That means there are 4 bets in the pot already.

Suppose there are 5 bets in the pot. What if opponent folds every time when a flush card hits?

By your reasoning
.2 * 0 + .8 * -1 = -0.8 eV

By my reasoning
.2 * 5 + .8 * -1 = 0.2 eV

So is calling a 1:5 payout with 4:1 odds slightly +eV or largely -eV?
Not sure I follow your example.....

I call the turn and the flush card hits. I bet the river and opponent folds. the EV of calling the turn is

(0.2*1) + (0.8* -1) = -0.6 EV

What you are doing is calculating the EV of the whole hand. What I am doing is calculating the EV of a call on the turn. Sure it is negative. Of course it is, we are behind and only 20% chance of winning. Ideally we would like to take a free card. We have already determined the pot is too big to fold, so we have to take the action which is the least negative.

Sure we will always reach the same conclusion, just have to be clear what we mean when we say EV. Is it the EV of the whole hand, or the EV of a particular action.
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euphoricism
Old 01-08-2007, 03:48 PM #14 (permalink)  
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The fact that this is a blind steal situation often throws logic to the wind.
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euphoricism
Old 01-08-2007, 03:52 PM #15 (permalink)  
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Well, whatever you do, don't fold. A raise isnt awful because its a blind situation, but I think a call is better.

Code:
Board:  	As Jd 4h 7s   	Pot:  	$6  	Call:  	$2  	Pot Odds:  	3 to 1
Results
Scenario 	You 	Opponent? 	Probability 	Win % 	Winning Probability 	Total Pot 	Expectation
1: 	Ks Js  	Ah 8d  	 50% 	 32% 	 16% 	 $8 	 $1
2: 	Ks Js  	Qs Jh  	 30% 	 88% 	 26% 	 $8 	 $2
3: 	Ks Js  	5s 5h  	 20% 	 95% 	 19% 	 $8 	 $2
Summary Results
Win Probability for this Scenario: 	 61% 	Total Expectation: 	 $5
Less: Break-even win% needed: 	 (25%) 	Less: Amount of Call: 	 ($2)
Positive  Variance: 	 36% 	Positive  Expectation: 	 $3
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bigspenda73
Old 01-08-2007, 10:10 PM #16 (permalink)  
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 Euph, where'd you get that program?
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