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Questions about Pot Odds and Expected Value

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Questions about Pot Odds and Expected Value - Tue Aug 05, 2014, 06:40 PM
(#1)
Glevcov's Avatar
Since: Aug 2014
Posts: 11
I'm currently studying the Cash Game course from PSO, but the article about Pot Odds and Expected Value left me with some doubts.

At some point, there's this:
Quote:
In that lesson, we calculated your odds of winning a hand in a percentage, but it can also be displayed as a ratio between winning and losing. A 20% winning probability can be translated as 4:1 odds - you will lose four in five times.
Which is right, as far as I understand.

But then, later on, they say:
Quote:
According to the chart above, your odds are 4:1 to hit your flush draw. The pot odds are higher. You should therefore call.

You can see why this call is correct by looking at the long-term picture. If you make this call four times, mathematics says that you will hit your draw once. That means you will win $5 for every $4 (4 * $1) you invest. That is good business.
Is this correct? Don't you actually have to make the call five times to hit a draw once, statistically speaking?

The same doubt is even worsened after they state this at some point:
Quote:
However, according to the table the odds of winning the hand are 11:1. You don't have the right pot odds to call here and should therefore fold.

Again, a glance at the long-term picture reveals why this is so. In this instance, you would need to play ten times in order to win $30. But those ten calls would cost you $50 ($5 * 10) and so this is not profitable.
In my mind the correct would be that you need to play twelve, not ten, times to win once.

So, am I misunderstanding something simple or there's a little mistake there in the article? Thanks in advance!
 
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Tue Aug 05, 2014, 07:36 PM
(#2)
ForrestFive's Avatar
Since: May 2011
Posts: 2,036
Hi Glevcov,

Not looked at the figures in the article but I did get confused with the wording when people talk about odds and outs. Maybe this is the same for you, sorry if I'm off track.

Your 4-1 to hit a flush are fixed Card odds, then...

Quote:
According to the chart above, your odds are 4:1 to hit your flush draw. The pot odds are higher. You should therefore call.

... the word higher meaning better Pot odds say for example 5-1 on your money.

So if the pot was $100 and you face a bet of $25 = 125/25 so 5-1 to make the call. So calling is a good financial decision.

Running it 5 times at this price is better than 4-1 where we know winning one in five is 20%.

Other PSO people will help you on this as I still get things mixed up.
 
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Tue Aug 05, 2014, 08:02 PM
(#3)
JWK24's Avatar
Since: Jun 2010
Posts: 24,831
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When looking at odds and outs, the quick rule is 2% equity per out per street and I use equities as they're easier for me to calculate.

For a flush draw (9 outs), I have an 18% chance to hit for each street... so I will hit the flush on the next street a bit less than 1 in 5 times.. which is close to 4 to 1 odds.

What I need to compare this to is the pot equity, to see if a play is profitable or not. To calculate the pot equity, it's (amount I need to put into the pot)/(total pot will be after my chips go in). For this, it will be 25/150 or 16.7%.

Since my hand equity (18%) is higher than my pot equity (16.7%).... I should call, as I expect to gain 1.3% each and every time that I call.

If the pot equity is higher, then I'd expect to lose chips.. so I'd want to fold.

Hope this helps and good luck at the tables.

John (JWK24)


Super-Moderator



6 Time Bracelet Winner


 
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Wed Aug 06, 2014, 12:40 PM
(#4)
Glevcov's Avatar
Since: Aug 2014
Posts: 11
Thanks guys! Both your answers were clarifying!

But just being a little more specific about notation, if I have hand odds of 11:1, that means I win one time for every 12 times I play, right?
 
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Wed Aug 06, 2014, 12:48 PM
(#5)
JWK24's Avatar
Since: Jun 2010
Posts: 24,831
(Super-Moderator)
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Quote:
Originally Posted by Glevcov View Post

But just being a little more specific about notation, if I have hand odds of 11:1, that means I win one time for every 12 times I play, right?
correct

John (JWK24)


Super-Moderator



6 Time Bracelet Winner


 
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Wed Aug 06, 2014, 05:19 PM
(#6)
ForrestFive's Avatar
Since: May 2011
Posts: 2,036
Hi Glevcov,

I read the article and see the contradiction. The author when talking Card odds:

Quote:
In that lesson, we calculated your odds of winning a hand in a percentage, but it can also be displayed as a ratio between winning and losing. A 20% winning probability can be translated as 4:1 odds - you will lose four in five times.

Then when talking Pot odds:

Quote:
According to the chart above, your odds are 4:1 to hit your flush draw. The pot odds are higher. You should therefore call.

You can see why this call is correct by looking at the long-term picture. If you make this call four times, mathematics says that you will hit your draw once. That means you will win $5 for every $4 (4 * $1) you invest. That is good business.

So it makes no sense to me. Do I make the call four in five times? To, on average win once with odds laid at 5-1 or are the odds 4-1?

Same with the gut shot example. We know its 11-1 on the cards. But why later state if you make this call 10 times? Is it over 11 trails?

 
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Thu Aug 07, 2014, 04:32 AM
(#7)
Glevcov's Avatar
Since: Aug 2014
Posts: 11
Yeah, thanks guys!

About the contradictions, at the end I think the author just mistyped some things. Then the correct notation is
number of losses:1, meaning that you have to play number of losses+1 times to win once. Examples:
A hand odd of 4:1 means you have to play 5 times to win once.
A hand odd of 11:1 means you have to play 12 times to win once.

That makes sense if you test and calculate your profit with some good pot odds.
 
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Thu Aug 21, 2014, 11:14 AM
(#8)
sparkes25's Avatar
Since: Feb 2013
Posts: 645
Just a small thing to add, the pot odds are the correct way to work out your odds of hitting the flush, but may not be the odds of winning the pot, for example, if the flop has 2 clubs and is paired and you hold 2 clubs in your hand, you have a 4-1 chance of hitting a flush but the flush may not be the winning hand even if it hits as you will not have the nuts.

Also if you hold 2 low clubs you may not have the best flush draw.

Lets say there is $5 in the pot, player 1 bets $5 and two players call, the action is on you, the flop is jj4 with 2 clubs and you hold 89 of clubs, you are getting 4-1 but due to the action and number of players in the pot you odds of winning would be less the 4-1. So even tho you have the 4-1 odds you could fold and I would expect it to be the correct fold in this case.

Please note I am not in any way an expert this is just imo
 

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