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Pot odds to call here?
Geralt
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February 18, 2015 - 6:54 am
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PokerStars Hand #130714937164: Tournament #1146604155, $0.45+$0.05 USD Hold'em No Limit - Level III (25/50) - 2015/02/18 12:28:32 CET [2015/02/18 6:28:32 ET]
Table '1146604155 5' 9-max Seat #7 is the button
Seat 1: kovr3534 (4200 in chips) 
Seat 2: MariuszMM (1215 in chips) 
Seat 3: monsch76 (8970 in chips) 
Seat 4: Millosz05 (1550 in chips) 
Seat 5: Neske72 (4005 in chips) 
Seat 6: VaNkaTa!112 (300 in chips) 
Seat 7: BubosBankaRN (1390 in chips) 
Seat 8: schmiddiii (1957 in chips) 
Seat 9: Geralt90210 (1400 in chips) 
schmiddiii: posts small blind 25
Geralt90210: posts big blind 50
*** HOLE CARDS ***
Dealt to Geralt90210 [Qc Kh]
kovr3534: folds 
MariuszMM: calls 50
monsch76: calls 50
Millosz05: calls 50
Neske72: calls 50
VaNkaTa!112: folds 
BubosBankaRN: folds 
schmiddiii: calls 25
Geralt90210: raises 300 to 350
MariuszMM: folds 
monsch76: calls 300
Millosz05: calls 300
Neske72: calls 300
schmiddiii: folds 
*** FLOP *** [Ah 9s 6d]
Geralt90210: checks 
monsch76: checks 
Millosz05: checks 
Neske72: checks 
*** TURN *** [Ah 9s 6d] [Jd]
Geralt90210: checks 
monsch76: checks 
Millosz05: bets 1200 and is all-in
Neske72: folds 


Hero: ???


I'm still a noob when it comes to pot odds and equity calculations.  If someone could help me figure this out and explain the math to me step by step and show the working I would REALLY appreciate it.  Thanks in advance! 
TheClubber
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February 18, 2015 - 12:09 pm
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In general when you have to call X  to win a pot of Y, the equity you need is X / (X + Y). Ex. if you have to call 100 to win a pot of 300, you need 25% equity to break even [100/100+300) =25%]

EV = 25% * 300 + 75%* (-100) = 75 – 75 = 0. 

 

In your example, you raised to 350 and 3 people called, one limper folded and the small blind folded, so the pot is 1475.

On the turn Millos bet 1200, but you only have 1050 left so you have to call 1050 to win 2525. The equity you need is 1050/(1050+2525) = 29.4%. 

 

Villain may be bluffing, but let's assume for now he has at least an ace. If he does, you can only win by making a straight. That means you only win with a Ten, so you have 4 outs. You know about 6 cards – 2i in your hand and 4 on the board, so there are 46 unknown cards. So the probability you make your straight is 4/46 or 8.7%. You clearly aren't getting the right price and shoudl fold. 

 

Say villain exposes his hand as J9s, you could also win with a K or Q. Then you would have 10 outs out of 46 or 10/46 =21.8% which is still not enough to call profitably..

======

Here's another approach:

You have 4 outs out of 46 cards, so the odds of you winning are 42:4 against or 10.5:1. To make a profitable call, you need to get paid at least 10.5:1. You have to call 1050, so the pot needs to be 11025 (1050*10.5) for you to make the call.

Again if he exposes his hand as J9s, you have 10 outs, so the odds of you winning are 36:10 against, or 3.6:1. You can only call if the pot is 3780 (1050*3.6)

======

The other thing to consider is that even if you are getting the right price to call Millos, you have to worry about the people behind you. If they enter the pot it increases your immediate odds, but decreases your equity in the pot.

BionicApe
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February 18, 2015 - 2:35 pm
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Good explanation Clubber.

I would only simplify the overall Equity:Pot Odds formula by saying:  If the percentage chance of winning the hand (equity) is greater than the percentage of money you need to put into the total pot (pot odds) then the outcome has positive expected value.

%Equity > %Pot Odds = +EV

%Equity < %Pot Odds = -EV

Fundamentally, a good wager is a wager with positive expected value.  This is almost always explained by describing coin flips.  Assuming you're using a standard coin your equity in a coin flip is going to be 50%  If you're betting $0.50 to win $1.00 then your pot odds are 50%.  This describes a break even wager, or a wager with zero expected value.

Equity 50% =  Pot Odds 50% = zeroEV 

Now if you use the same coin your equity is still 50% but if you only have to put in $0.40 to win a $1.00 then your equity, 50%, is greater than your pot odds, 40%, and you have a wager with positive expected value.

1.)  Equity 50% > Pot Odds 40% = +EV

 

This also works in the other direction.  Assume now that you're using a non-standard coin that's more heavily weighted on one side.  When this coin is flipped it lands on heads 60% of the time and tails 40% of the time.  Now if you choose heads your equity is 60%.  You can now make a $0.50 bet to win $1.00 giving you pot odds of 50% but since you are going to be winning an even money bet more than 50% of the time you have a wager with positive expected value.

2.)  Equity 60% > Pot Odds 50% = +EV

 

Of course you can flip those equations around to describe negative EV scenarios.

1.)  Equity 50% < Pot Odds 60% = -EV

or

2.)  Equity 40% < Pot Odds 50% = -EV

 

This same principle applies to poker.  

The number of outs you have describes your 'probability of winning' the hand or your 'equity' in the hand.  I highly suggest learning how to calculate your equity based on the number of outs as Clubber described above, but for the sake of simplifying this discussion you can refer to an 'odds chart' where this has already been calculated.  A quick internet search will lead you to a gazillion of these, for example: …..charts.php

–Using the hand above if we assume that Millosz05 has Ax in the hole, giving him a pair of aces and monsch76 folds then you need to beat a pair of aces and the only way you can do that is by making a straight.  To make a straight you need to hit a ten on the river giving you four outs.  Referring to the odds chart, 4 outs on the river gives you 8.67% equity.

 

To determine your pot odds you need to add up all the money in the pot, then add the amount you need to call the bet to the pot to determine the 'total pot' and then you divide the amount you need to call the bet by the 'total pot'.  Clubber gives this equation above, X/(X+Y) where 'X' is the amount you need to call the bet, 'Y' is the money currently in the pot and (X+Y) is the 'total pot' or how much will be in the pot if you decide to call the bet.

–Using the hand above:  The pot before betting on the river is 1500.  Milosz bets 1200, but since you only have 1050 left behind Milosz's bet can only be equivalent to your remaining chips.  1500 + 1050 = 2550(Y) in the pot before you decide to call and if you call there will be

1050(X) +2550(Y) = 3600(X+Y) so

X/(X+Y) = 1050/3600 = 29.2% Pot Odds

(note — Clubber and I both had to add up the total pot and we arrived at different values because one of us made an adding error.  It's conventional and considerate to state the value of the pot on each street when posting a hand to save the people reviewing the hand the trouble of having to do so — it's a small thing, but figuring out what happened in a hand can be challenging enough without having to do basic math.  The less you make your hand reviewers work, the more inclined they will be to provide detailed and thoughtful answers for you.)

 

Comparing your Equity in the pot to the Pot Odds you're getting,

8.67% Equity < 29.2% Pot Odds = -EV

It's clear that you're not even close to getting the 'right price' to call this bet.

 

It's imperative that you figure out how to do expected value calculations.  For the most basic explanation of pot odds and equity it's sufficient to know whether or not an outcome is positive or negative expected value.  But determining more precise approximations of expected value is essential for assessing different options and evaluating decisions.  

mhonan981
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February 18, 2015 - 3:39 pm
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Since Geralt is new to this, I think it is worth bringing up the “Rule of 4” and the “Rule of 2” for doing quick equity calculations in-game. It is not exact, but most of the time it will give you a close enough approximation to make the correct decision.

Rule of 4 – On the flop, multiply the number of outs you have by 4 to approximate your equity, e.g. you have a flush draw giving you nine outs = 9 x 4 = 36% equity (assuming your opponent has an overpair or something where you need to hit your flush to win)

Rule of 2 – Same as above, but on the turn your equity is cut in half. Multiply number of outs by 2; in your hand example you need a T, four of which remain, 4 x 2 = 8% equity.

We see from Ape and Clubber’s math above that the actual equity is 8.7%, but when dealing with in-game situations 8% is definitely sufficient.

Hope that helps.

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