Is Running it Twice a Sucker Bet? (Long)

[TrvChBoy]

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Is Running it Twice a Sucker Bet?

The newest poker television shows including GSN’s High Stakes Poker and UPN’s Cash Poker introduced us to the concept of Running it Twice. To Run it Twice, generally the following situation is present

The game is a cash game, not a tournament
The pot is heads-up (just two players)
One player is all-in
There is at least one more card to come

If both players agree to Run it Twice, the dealer deals the remaining cards twice. For example, if there is only one card left to come, the dealer would deal two separate river cards.

If one player wins with both river cards, that player wins the entire pot
If one player wins with one river card and the other player wins with the other river card, the pot is split.

The question I had when seeing this is: What is the advantage or disadvantage of this bet? I searched on the Internet and read a lot of opinions that there is no real advantage or disadvantage; it only reduces variance by increasing the chances of a split. I also wondered if there was more of an advantage if one player was a clear favorite. Of course, being from the Show-Me-State, I was frustrated with reading other people’s opinions on the subject, so I decided to calculate the Expected Value (EV) of running it twice.

EV is the correct way to calculate whether a bet is a sucker bet or not and it is as simple as multiplying the amount you expect to win by the probability of winning, then subtracting the amount you expect to lose multiplied by the probability of losing.

For example, the EV of betting $1 on red on an American roulette wheel is

Win: Red: +$1 x 18/38 = + $0.47
Lose: Black -$1 x 18/38 = - $0.47
Lose: Green -$1 x 2/38 = - $0.05
Total: = - $0.05

Since there are 18 reds, 18 blacks, and 2 greens out of 38 possible outcomes on the American roulette wheel.

So the EV of betting red on an American roulette wheel is -$0.05, and over a long period of spins, I expect to lose an average of $0.05 per spin. Since the EV is negative, this qualifies as a sucker bet. I may win any given bet, or any given night, or any given week, but over thousands of bets, I will lose, and at the end of thousands of bets I will have lost about $0.05 per spin.

EV is the correct way to evaluate any bet, and it is the correct tool to see if Running it Twice is a sucker bet or not.

For this investigation, I calculated the EV of six scenarios:

Running it Once as a Long Shot
Running it Twice as a Long Shot
Running it Once as Even Money
Running it Twice as Even Money
Running it Once as the Favorite
Running it Twice as the Favorite

For this test, I selected a heads-up Hold-Em game with $100 from each player in the pot and one card to come. In this situation, there are 2 cards in Player A’s hand, 2 cards in Player B’s hand, and 4 cards on the board for a total of 8 seen cards and 44 unseen cards.

For the long shot scenarios, I gave our underdog 4 outs to a win, consistent with an inside straight draw.

For the even-money situation, I gave each player 22 outs to a win, which might be impossible in Hold’Em, but is a good check on my math, since the EV must be exactly $0.00 for this perfect coin flip situation.

For the favorite scenarios, I gave our favorite player 40 outs to a win, which is consistent with a made hand threatened only by an inside straight draw. Notice that this is the exact opposite of the long-shot scenario, so it is another good check on my math; the EV for the favorite scenario must be the same number as the EV of the long-shot scenario, but the EV for the favorite scenario will have a positive sign.

I will leave the calculations in the files section for those who wish to review it. Here are my findings

Running it Once as a Long Shot (4 outs): EV -$81.82
Running it Twice as a Long Shot (4 outs): EV -$81.82

Running it Once as Even Money (22 outs): EV $0.00
Running it Twice as Even Money (22 outs): EV $0.00

Running it Once as the Favorite (40 outs): EV +$81.82
Running it Twice as the Favorite (40 outs): EV +$81.82

From this experiment, I conclude that there is no long-term financial advantage or disadvantage to Running it Twice. The EVs are the same whether you are way behind, looking at a coin flip, or way ahead.

One thing Running it Twice does do: It increases your chances of splitting the pot while at the same time decreasing your chances of winning or losing the entire pot.

Running it Once as a Long Shot (4 outs)

Win the pot: 9.1%
Split the pot: 0.0%
Lose the pot: 90.9%

Running it Twice as a Long Shot (4 outs)

Win the Pot: 0.6%
Split the Pot: 16.9%
Lose the Pot: 82.5%

To check my math, see the Excel spreadsheet at
http://www.saltlakepoker.com/poker/runningittwice.xls

So when running it twice as a long shot, you get the advantage of splitting more often, but you give up a considerable amount of your probability of winning the entire pot. Since the EV of Running it Once is the same as the EV of Running it Twice, there is no financial advantage or disadvantage in the long run, but you may appreciate the reduction in variance. When running it twice, your short-term fluctuations will be lower, but your long-term overall win or loss will be unchanged. It is desirable to reduce your short-term fluctuations when playing high for your bankroll, or when playing against opponents who are less skilled than you.

When you get the chance to run it twice, decide whether or not you want to decrease your chances of winning and increase your chances of splitting. If you do, then go ahead and run it twice…whether you are way behind, even money, or way ahead, I assure you it’s not a sucker bet.

Organizer Eric (Full Tilt: TrvChBoy)
http://poker.meetup.com/939/
nelsonericrobert@yahoo.com