davezz5, on Tuesday, March 21st, 2006, 5:45 PM, said:
Wouldnt you want to run it twice being a 2:1 dog? 2 chances of splitting the pot against sudden death.
I'll be glad to run it as many times as you like when I'm the 2:1 favorite. :DFirst off let me say I am not clear exactly the way running it twice works. Hopefully Daniel will read this thread and comment on the following analysis.Now, Daniel is about a 2:1 underdog on the flop when the money goes in. To simplify matters let's look at the following approximate
probabilities (I realize that if DN hits one or more of his outs in the first run then there are fewer outs for him to hit on the second run, but for now---to simplify things---we will ignore this subtlety):Daniel goes Win-Win: 1/3 * 1/3 = 1/9Daniel goes Win-Lose: 1/3 * 2/3 = 2/9Daniel goes Lose-Win: 2/3 * 1/3 = 2/9Daniel goes Lose-Lose: 2/3 * 2/3 = 4/9THEORY A: SPLITTING THE EXISTING POT BETWEEN THE RUNS
The pot is fixed once the money goes in (in this case it was $235.3k). Since the money went in after the flop was shown, only the turn and river cards are run twice. The winner of each run wins half the existing pot ($117.65k).Daniel goes Win-Win: 1/3 * 1/3 = 1/9 for $235.3k - $110k = +$125.3kDaniel goes Win-Lose: 1/3 * 2/3 = 2/9 for $117.65k - $110k = +$7.65kDaniel goes Lose-Win: 2/3 * 1/3 = 2/9 for $117.65k - $110k = +$7.65kDaniel goes Lose-Lose: 2/3 * 2/3 = 4/9 for -$110kDaniel's expectation: (1/9)($125.3k)+(4/9)($7.65k)+(4/9)(-$110k) = -$31.57k(For the record, this is what I believe they are doing.)THEORY B: PAYING THE ALL IN AMOUNT FOR EACH RUN
For the all in call, Daniel called $80k into a $155.3k pot. Here we will act as if each player will basically play the all in betting sequence twice with the same given flop. The pot then becomes $75.3k (preflop) + 4*$80k = $395.3k and each player wins half of the (new) TOTAL pot.Daniel goes Win-Win: 1/3 * 1/3 = 1/9 for $395.3k - $190k = +$205.3kDaniel goes Win-Lose: 1/3 * 2/3 = 2/9 for $197.65k - $190k = +$7.65kDaniel goes Lose-Win: 2/3 * 1/3 = 2/9 for $197.65k - $190k = +$7.65kDaniel goes Lose-Lose: 2/3 * 2/3 = 4/9 for -$190kDaniel's expectation: (1/9)($125.3k)+(4/9)($7.65k)+(4/9)(-$110k) = -$58.23k(I don't see how this is what they are doing since if one of the players is "all in", where do they get the money to "pay" for the second run?)WHAT ABOUT JUST RUNNING IT ONCE?!
Daniel's expectation: (1/3)($125.3k)+(2/3)(-$110k) = -$31.57kWhile this may surprise some, it doesn't surprise Daniel or any of the other pros! The reason they run it twice is their EV does not change---but running it successively does decrease
the variance.I would ALWAYS run it twice as a 2:1 fav!
I don't see why (other than pure gambling reasons) someone would choose to run it more than once as a 2:1 dog.
Just call me THE BANKER.