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Math Noob Pt. 2

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bigspenda73

01-09-2007, 11:24 PM Post subject: Math Noob Pt. 2

#1 (permalink)

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bigspenda73 will become famous soon enough

Well well well, I fell into a trap that I myslef am so against. I did not understand something and instead of trying to figure it out myself I came and asked for the answers. The answers were good; however, I can honestly say I did not learn from them much b/c I never worked the equations out myself.

So here I am, back at a square 1. This time I am going to present a situation and include my own calculations and I would hope some of the more veteran members would double check my calculations.

6max Hold'em
Hero is BN with

MP is a sane villian running 25/15 over 350 hands
1 fold, MP raises, 1 fold, Hero 3bets, 2 folds, MP calls

Flop(7.5SBs):

MP checks, Hero bets, MP raises, Hero calls

Turn(5.5BBs):

MP bets, Hero...(fold/call/raise)

Option 1: Fold
The pot is now 6.5BBs, Hero can believe he has at the very very least 7 non board pairing diamonds. In all likelihood hero has 12 or 15 outs.

EV calling=EPSx(outs/total cards)- Betx(Non outs/total cards)

If we call we will expect villian to bet the river making our EPS (expected pot size) will be 7.5BBs. Therefore:
7.5*(13.5/46)- 1*(32.5/46)=+1.5 BBs
Therefore, folding costs us 1.5BBs in the long run
We can also deduce that calling wins us 1.5BBs in the long run

Now, the real dilemna....
Option 2: Semibluff raising the turn bet
We must first place villian on a range here in order to determine the %'s he will call/fold/3bet to our turn raise. We must also determine what villian would suspect us to hold.

1. What do we know?
--We know we will need to improve to win the pot, this happens 13.5/44 of the time.
--We know villian has a semi-strong to strong hand.
--We know WE have played this hand like the nuts.
--We know villian is able to deduce this
--We know villian's range for opening in MP but not capping PF is the following: 66-QQ, A8s+,ATo+, KTs+,KJo+, QJs

2. What is the percentage that villian folds to the turn raise?
--Let's take a rough estimate and say villian folds 15% of the time to a turn raise. Basically, hands such as 66/77/99/TT/JJ. We are truly interested in the hands that beat us folding, not defense hands like KJ making a play at us.

3. I will not bluff at the river if I miss my hand. Any opponent who can call this turn raise will beat my hand UI on the river and will fold to my bluff on the river if he cannot beat my hand.

4. If I DO improve on the river my opponent will c/c a bet from me 60% of the time. I assume this b/c I feel my opponent can fold to an A/K river but not to a diamond.

5. After villian bets the turn the pot contains 6.5BBs.
a. If I call and improve my opponent will c/c the river meaning I will win 7.5BBs
b. If my semi-bluff induces a fold I win 6.5BBs
c. If my semi-bluff is called and I improve I win 8.1BBs
d. If my semi-bluff is called and I do NOT improve I lose 2 bets.

Deep Breath now....

We already know the ev of calling the turn bet=1.5BBs

Now we must calculate the EV of raising the turn if villian will fold 15% of the time.

EV= (.15*6.5)+(.85*(13.5/46)*8.1)+(.85*(32.5/46)*-2)
EV=+1.79BBs

+1.79>+1.5

Therefore, assuming villian will fold 15% of the time to our turn raise the semi-bluff is a more +EV play.

Anyone agree/disagree?
Anyone see any faulty calculations?
Anyone care?

'spenda

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sinky

01-10-2007, 09:29 AM

#2 (permalink)

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To make raising better than calling (when heads up) you must have > 50% chance of winning the hand. ie) for every chip you put in from this point forward you will get more than 1 chip in return. Forget what is already in the pot.

In this hand, given the betting, the best scenario is you have 15 outs against something like JJ. Your chances of having the best hand on the river are 15/46 = 32.6%. So you would have to have fold equity > 17.4%.

More likely you have between 9 and 12 outs giving you a ~23% chance of having the best hand on the river, so you would need your opponent to fold ~27% of the time to make a raise the best move.

Given that opponent raised pf, and check raised a drawless board and has now led the turn. I think he is rarely going to fold.

sinky

01-10-2007, 10:15 AM

#3 (permalink)

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Quote:

Originally Posted by bigspenda73

EV= (.15*6.5)+(.85*(13.5/46)*8.1)+(.85*(32.5/46)*-2)
EV=+1.79BBs

This is incorrect.

I think you are trying to say that 15% of the time opp will fold, of the remaining 85% of the time you will either win on average a further 2.6BB or lose 2BB if you miss. You have not actually included the odds of you winning/losing. And when you win you are counting all the bets in the pot, but when you lose you are only counting your bets on the turn.

I hate incuding the pot in EV calculations when you are simply trying to decide between a call and a raise. The only thing that should concern you is which choice will win you more (or lose you less) from this point forward. Using your assumptions,

EV of raising turn....
EV = (0.15*1BB) + (0.85*0.3*2.6BB) + (0.85*0.7*-2BB) = -0.377

wheras EV of calling is
EV = (0.3*2BB) + (0.7*-1BB) = -0.1

I would strongly recommend reading Small Stakes Holdem. It explains in detail all about equity and EV.

bigspenda73

01-10-2007, 12:14 PM

#4 (permalink)

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Sinky, i have included the chances of winning, its 13.5/46. That is the amount of outs I assume I have divided by the cards left in the deck.

On the other point. I believe I am correct in using the entire pot. I KNOW for certain i am correct in using it the 15% of the time our opponent folds a better hand such as 66 on the turn. That is the whole reason to raise the turn, to get our opponent to fold a better hand and winning w/o having to improve. As for the rest of the equation, I'd like to here other opinions (using entire pot) on that.

bigspenda73

01-10-2007, 12:46 PM

#5 (permalink)

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Alright, on the drive to work I was thinking about it and I have reaffirmed my calculations in my head. I hope this makes sense.

On the turn there is a 13.5/46 chance that we will improve and win the pot (Im saying 13.5 because there is a 50/50 chance that villian holds one of our cards plus a card on the board which would leave us only 12 clean outs).

All of the bets already in the pot are in the pot. By that I mean, they are no longer our bets or his, they are a sunk cost.

Our opponent leads the turn. AFTER he does this, the pot is a certain size. I believe 6.5BBs. From this point on I can win this amount of money or lose whatever I put into the pot. That is why I can include the entire pot in what I can win and only the additional bets I am placing in the pot in what I can lose.

In english my equations mean this:

EV= (.15*6.5)+(.85*(13.5/46)*8.1)+(.85*(32.5/46)*-2)

(.15*6.5) This means that when our opponent does fold (15% of the time) we win the entire 6.5BB pot straight up.

(.85*(13.5/46)*8.1) This mean that 85% of the time our opponent will call the turn. When he does we have a chance to win the pot 13.5/46 of the time. The total BBs we will win will be on average 8.1BBs. The 8.1BBs is determined by the fact that our opponent will pay off a diamond but not an A/K on the river.

(.85*(32.5/46)*-2) This means that 85% of the time our opponent does not fold the turn and we lose the pot 32.5/46 of the time. When this happens our play loses us 2 BBs.

All of these added together get EV=+1.79 to raise the turn.

Directed right @Sinky: You have to use the pot in EV calculations. Otherwise how could you ever call a flush draw on the turn?

sinky

01-11-2007, 09:14 AM

#6 (permalink)

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Quote:

Originally Posted by bigspenda73

Directed right @Sinky: You have to use the pot in EV calculations. Otherwise how could you ever call a flush draw on the turn?

Sorry but you have missed an important point. In a reply to your earlier post and this one, I stated that this is a decision between calling and raising. We have already determined that folding is not an option. (Pot odds clearly better than hand odds) Once the pot has determined that folding is not an option, it then becomes irrelevant when deciding between calling or raising. The money already in the pot will be constant regardless of a call or a raise. The EV calculation then concentrates only on the turn and river betting and is therefore much simpler.

Your conclusion .....

Quote:

Originally Posted by bigspenda73

EV= (.15*6.5)+(.85*(13.5/46)*8.1)+(.85*(32.5/46)*-2)
EV=+1.79BBs

+1.79>+1.5

Therefore, assuming villian will fold 15% of the time to our turn raise the semi-bluff is a more +EV play.

This is clearly wrong. Taking your numbers, odds of having the best hand 29.3% (13.5/46) added to the odds he will fold 15%, then you have a total chance of winning of 44.3%.

Your hands equity is 44.3%. Your return for a call or a raise will on average be 44.3% of all the bets that go in on the turn and river. Since you will contribute exactly 50% of these chips then you have an equity deficit of 6%. To put it another way, when you are the underdog you want to put in as few chips as possible. When you are favorite then keep raising.

euphoricism

01-11-2007, 05:45 PM

#7 (permalink)

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Spenda your theory is correct but your math is wrong.

I dont think "(.85*(13.5/46)*8.1) This mean that 85% of the time our opponent will call the turn. " is correct. I dont think its necessary at all. If he's folding 15% we dont need to factor that he's calling the other 85%.

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euphoricism

01-11-2007, 05:56 PM

#8 (permalink)

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(.15*6.5) we win if we raise is incorrect as well -- we've put more money in the pot and it aint ours once we do so. its (15*8.5)

Pot is 5.5, he bets, throws one chip out there. (Pot is 6.5) We raise and put two chips (8.5), so if he folds there its 15% of the time we win 8.5BB. If he calls the pot is then 9.5BB.

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bigspenda73

01-11-2007, 06:26 PM

#9 (permalink)

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Thanks for the replies.

Now my defense to both of them.

Sinky, my winning percentage may be 44% of the time. However, you have to use the pot size in this to determine the EV of it. If I steal this pot on the turn there is 15% of the time I win 6.5BBs where I would have never won any money at all. Just b/c my overall chance of winning the pot is 44% does not mean it is -EV to raise.

@Euph
Euph, the entire equation as a whole has to be relevant. This whole equation is determining the worth of a turn raise. This means I have to use .15 and .85 in the full equation.

@your second post- Also incorrect as if we win 15% of the time our 2BBs really never hit the pot. We wagered 2 to win the entire pot. The loss of 2 is addressed later in the EV equation.

We need to look at this equation as a whole, not as individual parts. The equation tells a story of all possible events. That is why it is tough to break it apart seperately.

koolmoe

01-11-2007, 09:12 PM

#10 (permalink)

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The calculations look correct based on your assumptions.

The only thing you haven't considered is that raising reopens the betting, and that has implications. Some percentage of the time, your opponent will have a hand that he might three bet the turn with (any set, two pair, Qdxd maybe), which makes your semibluff even more costly. Those hands affect your outs, but I'm assuming you took that into account with your 13.5 outs estimate.

Anyway, it's pretty trivial that raising with 12 or more outs on the turn is a hugely +EV thing to do, because you get a big discount on your bluff. There are also metagame aspects, which can be very positive so long as you remain aware of how aggressive semibluffing affects your image. If you run this semibluff often, you should never slowplay a big hand in a similar spot.

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euphoricism

01-11-2007, 10:04 PM

#11 (permalink)

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OK I just have to do it myself.

EV of a call is
(.3*8.5) - (.7*1) =
2.55 - .7 = +1.85bb

Now for comparison sake, lets do a raise with absolutely no folding equity (villain calls 100%). Well the pot will be around 10bb depending on if villain c/f's or c/c's river.

(.3*10) - (.7*2) =
3 - 1.4 = +1.6bb

So its slightly less EV to raise here if youre called 100% of the time. But put in some chance of villain folding (and no chance of being reraised, which is key), and we go way, way up.

EV of raising with 15% folding equity and villain will NEVER threebet:

.15[(1*6.5)]+.85[(.3*10bb)-(.7*2)bb)] =
.975 + .85[3 - 1.4] =
.975 + 1.36 = +2.33bb

Making villain fold is nice.

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bigspenda73

01-11-2007, 10:14 PM

#12 (permalink)

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Quote:

Originally Posted by euphoricism

Making villain fold is nice.

Yup.

Breakeven in my calculations is about 9% of the time. So if villian folds a better hand 9% of the time on the turn we break even. This takes reads but I believe the benefits are worth it.

euphoricism

01-12-2007, 12:15 AM

#13 (permalink)

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Do it with a 9 out draw, instead of 12, hows it change?

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bigspenda73

01-12-2007, 12:33 AM

#14 (permalink)

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Quote:

Originally Posted by euphoricism

Do it with a 9 out draw, instead of 12, hows it change?

Bluff would have to work more.

Pot size is a variable as well.

I'd work it with different numbers but I think the concept has been proven...

euphoricism

01-12-2007, 01:54 AM

#15 (permalink)

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Well I recall a thread from a LONG time ago where I did this exact thing with 9 outs and it was shown that I was wrong. So theres an optimal area that this is "doable"

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bigspenda73

01-12-2007, 02:03 AM

#16 (permalink)

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Hell yea, when opponent folds 100% of the time a bluff is always optimal.

On a serious note, let me run needed pot size calculations. The only problem is as pot size increases opponents willingness to fold has to decrease. I'd like to see that original post as well.

sinky

01-12-2007, 12:29 PM

#17 (permalink)

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Quote:

Originally Posted by bigspenda73

Sinky, my winning percentage may be 44% of the time. However, you have to use the pot size in this to determine the EV of it. If I steal this pot on the turn there is 15% of the time I win 6.5BBs where I would have never won any money at all. Just b/c my overall chance of winning the pot is 44% does not mean it is -EV to raise.

ok, I'm still learning. I think I can see where I have picked this up wrong. The discussions in SSHE about EV and equity edges are generally about multiway pots against poor opponents who will not fold.

Quote:

Originally Posted by euphorism

OK I just have to do it myself.

EV of a call is
(.3*8.5) - (.7*1) =
2.55 - .7 = +1.85bb

I am not sure where you are getting the 8.5 from. There are currently 6.5 BB in pot. Where are the additional 2 bets of profit coming from. If you call and hit the river are you assuming opponent will bet again and call a raise.

euphoricism

01-12-2007, 05:39 PM

#18 (permalink)

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Currently 5.5 in the pot
Villain bets (6.5)
We call (7.5)
Villain leads river (8.5)
We raise (10.5)
Villain calls (11.5)
OR
Villain check calls river (we lead, 8.5, he calls, 9.5 but I dont think you count our last one since theres no future betting on it, hence 8.5)

Its probably higher than 8.5, it could be pushing 11. Implied odds are tricky to quantify.

Edit: ignore this, it is horribly misguiding. I'm answering a question that wasnt asked.

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koolmoe

01-12-2007, 07:52 PM

#19 (permalink)

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Quote:

Originally Posted by euphoricism

Villain check calls river (we lead, 8.5, he calls, 9.5 but I dont think you count our last one since theres no future betting on it, hence 8.5)

euph, with all due respect, I think you are getting a little confused between pot equity and EV. Anyway, there's a pretty good example of how to calculate the EV of a semibluff on p. 100 of ToP. Also, there's an EV example on pp. 24-25 of SSH that clearly shows you should not count your bets in the positive portion of the EV calculation.

Quote:

Originally Posted by euphoricism

EV of a call is
(.3*8.5) - (.7*1) =
2.55 - .7 = +1.85bb

This equation is a bastardization of EV and pot equity. Your pot equity is (0.3*pot). Assuming that you will win a single bet on the river every time you make your hand, your EV should be (0.3*7.5 - 0.7*1) = 1.55 BB.

To see this, assume that the pot is $65 after your opponent bets the turn, and your stack is $100. If you call, the pot is now $75, and your stack is $90. Then, when you hit your hand, your opponent will check and call, making the pot $95, and your stack $80. The dealer pushes you the pot at showdown, making your stack $175. When you lose, you invest nothing else, and your stack remains at $90. So, you will profit $75 thirty percent of the time and lose $10 seventy percent of the time if you call the turn bet.

If you repeat the scenario 100 times, you profit $2250 the thirty times you win and lose $700 the seventy times you lose, for a net profit of $1550, or $15.50 (1.55 BB) per hand.

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bigspenda73

01-12-2007, 08:01 PM

#20 (permalink)

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I want koolmoe's powers of explanation; that is a great way of looking at pot equity vs. EV

And sinky, I'm glad you weren't too hardheaded to understand the differences, its cool to see this thread didn't end in any bloodshed.

Anyways, just to let anyone who questions this in the future know that this is a complex topic I took from Weighing The Odds by King Yao. I've doubled checked my original work and I can say that everything matches except for the variables (outs and pot size).

euphoricism

01-13-2007, 12:19 PM

#21 (permalink)

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Quote:

Originally Posted by koolmoe

Quote:

Originally Posted by euphoricism

EV of a call is
(.3*8.5) - (.7*1) =
2.55 - .7 = +1.85bb

I dont see how. Going into the turn the pot is 5.5 bets. Villain leads, making 6.5. The EV of our call would be the (.3*6.5 + any bets we expected to win on the river) - (.7*1 bet it costs to call). Ah I see. Youre assuming villain check/calls whenever a diamond hits. I didn't. I assumed villain would bet/call if we haven't shown resistance -- which I think he will far do far more often than he c/c's or b/f's.

My previous post is correct, but you're right I gave an implied odds answer and he asked an EV question. Oops.

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koolmoe

01-13-2007, 11:21 PM

#22 (permalink)

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Quote:

Originally Posted by euphoricism

Villain check calls river (we lead, 8.5, he calls, 9.5 but I dont think you count our last one since theres no future betting on it, hence 8.5)

I see you edited the post that contained this line, which is where I was getting confused about what you were doing. If you assumed winning two bets on the river every time, we're on the same page then

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