Mrg4540
Mrg4540
Joined: Sep 15, 2021
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September 15th, 2021 at 8:55:33 AM permalink
This problem has been driving me and my friends crazy.

Imagine a set over set situation, all in on the flop. The lower set only has 1 out to make quads and win. I know that typically, running it twice does not change the EV and only serves to minimize variance. However, in this situation, in which if you win the first run out, you have 0% chance to win the second board, does it behoove the person behind to only run it once? Remember, there is no replacement of the key card.

Proofs would be most welcome.

Thank you.
Deucekies
Deucekies
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September 15th, 2021 at 10:16:17 AM permalink
With only a roughly 4% chance on the flop to win, I'd say they should certainly be begging to run it twice. Maybe even three or four times even though they can only win once, just because something is better than a 96% chance at nothing.

I'd say the player with the higher set should only run it once, or offer to run it four times, guaranteeing themselves 3/4 of the pot.
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
kalc
kalc
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September 15th, 2021 at 10:34:07 AM permalink
It doesn't matter. Let's say there are only two players, so there are 44 cards left in the deck once one card is burned and the flop is dealt. To make the math simple, let's say that the burned card is the 4th card of the higher set, so that when the lower set makes quads, it always wins. We also remove any possible backdoor straight and flush draws.

For example: AsAd vs 7h7c. Flop is Ac7s2h. The burn card is the Ah.

The lower set has 4.545% equity in this pot, or exactly 1/22.

What happens if we run the turn and river 22 times?
unJon
unJon
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September 15th, 2021 at 3:16:28 PM permalink
I agree it has the same EV of running once or twice.

Assume pot is $100 for convenience. Also assume that no board straight or flush possible, so no chop pots.

Run once:

Lower set wins if he gets quads and higher set does not get quads: 2*1/45*43/44 = 4.3434% for EV of $4.34

Run twice:

The first run is same as above but only $50 at stake so EV = 4.3434% * $50 = $2.17

Second run has a few different situations:

A) first run had two blanks, which happens 43/45*42/45 = 91.21% of the time. Then the lower set wins 2*1/43*41/42 = 4.5404% of the time. Total EV contribution of: $50*91.21%*4.5504% = $2.07.

B) first run gave lower set quads so impossible to win second run. Total EV contribution of $0. (Note a small fraction of this scenario had the higher set also making quads, but we dealt with that already in calculating EV of first run).

C) first run gave higher person quads but not lower person, which happens 2*1/45*43/44 = 4.3434% of time. Then lower set wins 2*1/43 = 4.6512% of the time. Total EV contribution of: $50*4.3434%*4.6512% = $0.10

So EV of run twice is $2.17 + $2.07 + $0.10 = $4.34


EV is exactly the same between run once and run twice of $4.34.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Mission146
Mission146
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September 15th, 2021 at 3:27:59 PM permalink
Why run anything if not run it once if you are the favorite? I wonder if the underdog would accept it if the favorite offered EV, straight up. Known cards only.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
SOOPOO
SOOPOO
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September 15th, 2021 at 3:33:10 PM permalink
I read question. Took one second to figure out that EV is the same no matter how many times you run it. Obviously the more you run it affects variance, not EV.
unJon
unJon
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September 15th, 2021 at 3:47:10 PM permalink
Quote: SOOPOO

I read question. Took one second to figure out that EV is the same no matter how many times you run it. Obviously the more you run it affects variance, not EV.

  • link to original post

    Sure but OP asked to see the math.
    The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
    unJon
    unJon
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    Thanks for this post from:
    Mission146
    September 15th, 2021 at 4:01:10 PM permalink
    Quote: Mission146

    Why run anything if not run it once if you are the favorite? I wonder if the underdog would accept it if the favorite offered EV, straight up. Known cards only.

  • link to original post



    They have programs for playing online that will tell you how you are running vs EV. Can be pretty interesting.
    The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
    Mission146
    Mission146
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    September 15th, 2021 at 4:10:47 PM permalink
    Quote: unJon

    Quote: Mission146

    Why run anything if not run it once if you are the favorite? I wonder if the underdog would accept it if the favorite offered EV, straight up. Known cards only.

  • link to original post



    They have programs for playing online that will tell you how you are running vs EV. Can be pretty interesting.
  • link to original post



    Yes, and you can also get W/L/T percentage just from the WoV Calculator, so you could use that to calculate your equity in the pot. Rather than run it two, three, four or twenty-seven times, I wonder if anyone would ever agree to spilt based on EV.
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
    Dieter
    Administrator
    Dieter 
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    Thanks for this post from:
    Mission146
    September 15th, 2021 at 7:54:35 PM permalink
    Quote: Mission146

    Why run anything if not run it once if you are the favorite? I wonder if the underdog would accept it if the favorite offered EV, straight up. Known cards only.

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    The value may be in influencing the emotional state of the opponent, not in chips on the table.
    May the cards fall in your favor.

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