Call losing bets?

Tater10 · #1 08-23-2007, 11:39 AM

Ever have brain farts? I'm having one now.

Suppose you are on a gutshot draw to the nuts after the turn card comes. This is the only way you win.

Pot is $420

4 cards help out of 46 = 1 in 11.5, or 10.5 to 1 to hit

Your opponent bets all in $80 - giving you odds of 500:80 or 6.25:1.

Do you call?

If you fold, you give up 4/46*500 = $43.48 in equity
If you call $80, you give up 42/46*$80 = $73.04, but now have the right to 4/46*500 or $43.48, so you only lose ($73.04-$43.48)=$29.56?

In other words, it's a losing situation, but you will lose less by calling?

What am I missing?

mykey1961 · #2 08-23-2007, 12:37 PM

Your numbers are comparing apples and oranges.

The "standard" way of calculating is to assume folding at that point is 0 EV. (4/46*580)-80 = -29.56.

It costs you $80 to have a 4/46 shot at a $580 pot.

Another way of looking at it is to figure how much you have invested in the pot so far, and how much you could ultimately pull out of the pot.

Lets assume you've invested $150 into the $420 pot.

If you fold now, you net -$150 for the hand.

If you choose to call. 10.5 times you will lose $230 (10.5*-230=-2415), and 1 time you will win a pot worth $580 for a net win of $350.

(-2415+350)/11.5 = -179.56

So your choice is Fold and lose on average $150 per hand
or call and lose on average $179.56 per hand.

Tater10 · #3 08-23-2007, 01:12 PM

Ok, I guess I'm just looking at it differently.

How about this scenario:
There is a party in Las Vegas that will pay 1 in 10 people $1000. Cost to go is $90.

You figure this is +EV so you decide to go.

When you get there, you realize you forgot your ticket. For $50 they can re-issue your ticket (you can not get your $90 back).

Should you pay the $50 or just leave?

DarkMagus · #4 08-23-2007, 01:58 PM

[ QUOTE ]
Ok, I guess I'm just looking at it differently.

How about this scenario:
There is a party in Las Vegas that will pay 1 in 10 people $1000. Cost to go is $90.

You figure this is +EV so you decide to go.

When you get there, you realize you forgot your ticket. For $50 they can re-issue your ticket (you can not get your $90 back).

Should you pay the $50 or just leave?

[/ QUOTE ]

The $90 is a complete loss. Since you cannot get it back, no matter what happened, it's no longer relevant. So now we have a new situation where we're being offered 20-1 odds on something that's a 9-1 shot. Easy call.

mykey1961 · #5 08-23-2007, 03:03 PM

[ QUOTE ]
Ok, I guess I'm just looking at it differently.

How about this scenario:
There is a party in Las Vegas that will pay 1 in 10 people $1000. Cost to go is $90.

You figure this is +EV so you decide to go.

When you get there, you realize you forgot your ticket. For $50 they can re-issue your ticket (you can not get your $90 back).

Should you pay the $50 or just leave?

[/ QUOTE ]

Purchasing the original ticket for $90 is not -EV unless you expect to forget the ticket more than 1 time in 9.

Purchasing the reissued ticket for $50 is +EV.

Forgetting the ticket is equivilant of QQ flopping AKJ after being reraised preflop.

tarheeljks · #6 08-23-2007, 03:32 PM

the ticket that has all ready been purchased is a sunk cost

rufus · #7 08-23-2007, 05:06 PM

[ QUOTE ]

In other words, it's a losing situation, but you will lose less by calling?

What am I missing?

[/ QUOTE ]

There are situations where you should call while behind (a $20 all-in raise here, for example).

However, you're double-counting the pot equity - once as a potential loss, and once as a potential win. If you consider yourself to be losing the pot equity when you fold, then you shouldn't be considering it a win when you call.

580*4/46 (pot equity) - 80 (cost of call) = -$30
Folding
0 (pot equity) - 0 (cost to fold) = $0

Since the opponent is all-in, there's no implied odds. (If your opponent were willing and able to put $315 in on the river if the gutshot hit, you'd break even.)

AaronBrown · #8 08-23-2007, 09:16 PM

There is a famous example relating to the party problem.

(A) You buy a ticket for $100 to hear your favorite music performer. You're about to leave, when you realize you left the ticket at work, and don't have time to go get it. You cannot get a refund. You can go to the theater and buy another $100 ticket. Do you go?

(B) You didn't buy a ticket in advance for the show, you're planning to go and pay $100 for the ticket.You're about to leave, when you realize you've got a $100 parking ticket, which you have to pay. Do you go?

Most people say they wouldn't go in (A), but don't understand why someone wouldn't go in (B). To an economist, the two situations are identical.

rufus · #9 08-24-2007, 11:13 AM

[ QUOTE ]
There is a famous example relating to the party problem.

(A) You buy a ticket for $100 to hear your favorite music performer. You're about to leave, when you realize you left the ticket at work, and don't have time to go get it. You cannot get a refund. You can go to the theater and buy another $100 ticket. Do you go?

(B) You didn't buy a ticket in advance for the show, you're planning to go and pay $100 for the ticket.You're about to leave, when you realize you've got a $100 parking ticket, which you have to pay. Do you go?

Most people say they wouldn't go in (A), but don't understand why someone wouldn't go in (B). To an economist, the two situations are identical.

[/ QUOTE ]

Actually, those two situations are (somewhat) different:
The value of paying the parking ticket can be much higher than the value of going to the concert, and the value of having money is not linear with the amount of money you have. So, for example, if you're on a monthly budget, you might not have 'entertainment funds' left for the second concert ticket, but paying the parking ticket is sufficiently valuable that you pay it using emergency funds.