Gaining an Advantage Running it Twice

Consider a situation in Texas Hold 'Em where three players are in the hand and at least two are all in after the flop. It may be agreed that they "run it twice," meaning they divide the pot in two and deal two separate sets of turn and river cards, each set determining who wins half of the original pot. This does not change the expected value of anybody, but does lower variance. All players must agree to run it twice to do so, otherwise it is run once only.

However, consider the situation where what I'll call Player 1 wants to run it once only. Player 2 then offers to Player 3 to run it twice, before the turn is dealt, assuming Player 1 doesn't win. Should Player 3 accept?

Your immediate response might be that the expected value is the same and that it doesn't make any difference. However, it can and probably does.

Consider this situation:

Board : Qd,2c,10c

Player 1: Ac, 8c
Player 2: Qh, Qs
Player 3: Kc, 5c

In this situation, player 3 should absolutely accept the offer.

Why? Basically, player 3 is dominated by player 1. If player 1 were somehow out of the situation, he would have a much better chance, winning in most situations with any club on the turn or river.

Let me prove it with my Texas Hold 'Em Calculator.



Here the expected values are:

Player 1: 20.60%
Player 2: 77.41%
Player 3: 1.99%

However, if we take player 1 out of it, they become:

Player 2: 78.41%
Player 3: 21.59%



Player 3's equity improves tremendously under the offer. Granted, it doesn't go up to exactly 21.59%, but more. This is because if player 1 doesn't win, it means cards other than clubs were dealt on the turn and river the first time, leaving a club rich deck for the second and third times.

In conclusion, if you're ever in this situation and the rules allow for it, be careful. Any expected value gained by one player will be lost by another. If someone made this offer to me, I would probably decline, assuming he is trying to pull this trick to his advantage. However, you might make the offer if you're clearly in a dominated position.

This post was largely inspired by a similar one at Two Plus Two Forums.

Are you assuming that the players get to see each others cards before making that determination? If so, my assumption is that it would not matter if they didn't see each others cards first.

Quote: DRich

Are you assuming that the players get to see each others cards before making that determination? If so, my assumption is that it would not matter if they didn't see each others cards first.
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Yes, I am assuming that. I agree that it wouldn't matter if you didn't, assuming you couldn't infer anything by how the betting went down.

Quote: DRich

Are you assuming that the players get to see each others cards before making that determination? If so, my assumption is that it would not matter if they didn't see each others cards first.
link to original post

this question is so fitting relative to the game wasioux

Quote: heatmap

Quote: DRich

Are you assuming that the players get to see each others cards before making that determination? If so, my assumption is that it would not matter if they didn't see each others cards first.
link to original post

this question is so fitting relative to the game wasioux
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Do you know that other than the creators of the game you are the only one that has ever mentioned WaSioux to me?

Quote: DRich

Quote: heatmap

Quote: DRich

Are you assuming that the players get to see each others cards before making that determination? If so, my assumption is that it would not matter if they didn't see each others cards first.
link to original post

this question is so fitting relative to the game wasioux
link to original post

Do you know that other than the creators of the game you are the only one that has ever mentioned WaSioux to me?
link to original post

its just a fascinating game imo. its fascinating that i can talk to you about it. the patent is amazing. the video is amazing. its just been a delight to my life ever since ive found it. ive since found ONE patented algorithm that is almost like the one for wasioux but its nothing like it.

I hope you also know that the patent is still being used to this day... a developer who frequents this forum apparently uses it in a live casino game to this day and most likely for a while as they were just approved for play in casinos i think at the start of this year.

Quote: heatmap

I hope you also know that the patent is still being used to this day... a developer who frequents this forum apparently uses it in a live casino game to this day and most likely for a while as they were just approved for play in casinos i think at the start of this year.

I was not aware but I would be interested in hearing about the game. The patent is probably indefensible as it was written too specifically. I do think the concept and game was interesting but it did very poorly in the field trials.