Math Question

[PokerFink]

This is a fairly simple math question that I should probably be able to figure out myself, but I'm going to ask to make sure I do it right.

I hold a small pair. My single opponent is all-in, and I am getting exactly 2:1 on my call. I feel that sometimes it will be a race, and sometimes I will be against a bigger pair. I will never be ahead of smaller pair.

To make it easy, let's assume I'm either exactly 50% to win or exactly 20% to win depending on what villian holds.

What % of the time must this situation be a 50/50 race for the call to be +EV?

[ QUOTE ]

I hold a small pair. My single opponent is all-in, and I am getting exactly 2:1 on my call. I feel that sometimes it will be a race, and sometimes I will be against a bigger pair. I will never be ahead of smaller pair.

To make it easy, let's assume I'm either exactly 50% to win or exactly 20% to win depending on what villian holds

[/ QUOTE ]

I always get confused by the ratio odds notations stuff. If 1:2 means that, if you win you net your bet, then you need the outcome to be 50/50 all of the time to win. If it means that you net twice your bet if you win, then you you need to have a 50/50 chance 10/18 (slightly more than half) the time for the EV to be zero.

[UATrewqaz]

If my math is right you need to be in a race situation at least 45% of the time to break even. Anything above .45 should be +EV.

Here is my calculation

When it is a race your EV calculation is

(.5) * 2 + (.5) * -1 = .5

When you are behind a bigger pair the EV calculation is

(.2) * 2 + (.8) * -1 = -.4

Thus the +EV of the race situation is greater than the -EV situation of the smaller pair situation.

.5 ( .45) = .4 (.55)

Thus a .45/.55 ratio is the break even point.

If you opponent has 2 overcards more than 45% of the time you can label this a +EV situation, anything less is a -EV situation.

[PokerFink]

(.5) * 2 + (.5) * -1 = .5 is...

(My equity) * (My pot odds) + (His Equity) * (-1)

So if I were getting 3:1 instead of 2:1 it would be

(.5) * 3 + (.5) * -1 = 1

Is this right?

[PokerFink]

[ QUOTE ]
I always get confused by the ratio odds notations stuff.

[/ QUOTE ]

I was getting 2:1. That means there was 2 dollars in the pot (including villian's bet) and I had to call 1 dollar. When I win, I win 2 dollars. When I lose, I lose 1 dollar.

[UATrewqaz]

Correct,

when getting N:1 you can see how you a lower % of equity is needed to get +EV, because your loss is constant but the bigger the N the bigger the profit, so if you were getting 99:1 on a bet you'd really only need a 1% chance of winning to just break even

.01 * 99 + .99 * -1 = 0

[DavidC]

Edit: Ahem... It's late (early)... This post was made under the assumption that we're in the BB and SB raises all-in when we have 33.


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EV in the race: 4(0.5)-1 = +1
EV in the domination: 4(0.2)-1 = -0.2

Is this correct?

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X(1) - Y(0.2) = 0

X - 0.2*Y = 0

X = 0.2*Y

Y = 5X

Therefore if you're behind 5/6 times or less you can call?

Let's try this:

1(1) -0.2(5) = 0... Yeah, that looks about right.
1(2) -0.2(4) > 0... booyah!

[DavidC]

EV(race): 3(0.5)-1 = 0.5
EV(dominated): 3(0.2)-1 = -0.4

0.5X -0.4Y = 0
0.5X = 0.4Y
X = 0.8Y
Y = 1.2X

Therefore X is 1/2.2 and Y is 1.2/2.2

Therefore you need to be ahead 45.45% of the time.