Quote:
Originally Posted by Fore
Your logic here is just bad. Rit does not impact your long term ev. Only impacts the variance getting too the long term.
I think all he is really saying is "it is harder for the underdog to hit twice"... so he doesn't mind running it twice when ahead since getting scooped is unlikely, but runs it once when behind since scooping it twice as the underdog is hard, so may as well go for the glory of binking it once.
It's kind of a strange risk philosophy, but yeah if he was using "favorable" to mean +EV then of course that is nonsense.
For anyone who doesn't see why it is the same EV, think about what would happen with all in of a pair vs a flush draw (no overcards) on the turn.
There are 44 unknown cards left and for simplicity let's say the game is heads-up and the dealer isn't burning cards between streets. So the flush draw has 9/44 outs.
If you run it once, there is a 9/44 chance the flush wins the full pot. So EV is (20.45%*1)+(79.55%*0) = 20.45%
What if you run it 44 times? The flush will win 9 times and the pair will win 35 times and there is a 100% chance that the flush will get 20.45% of the pot with the chop. That's basically an equity chop and removes all variance.
Running it twice is just a subset of that extreme "running it 44 times" scenario.
There's a (9/45)*(8/44) or 3.8% chance the flush hits both rivers. There's a (9/45)*(35/44) or 16.65% chance the flush wins the first river and loses the second, but order doesn't really matter so there's another 16.65% chance the flush loses the first river but wins the second. Finally there's a (35/44)*(34*43) or 62.90% chance the flush misses both times.
So the flush draw has a 37.1% chance of winning at least half of the pot, an "improvement" over the 20.45% chance of winning it all when running it once. Variance is lower because they will get stacked less frequently, but they also only get to scoop the pot 3.8% of the time vs 20.45% of the time if they run it once.
But the equity is (3.8%*1)+(33.3%*0.5)+(62.90%*0) = 20.45% again
I know that's probably obvious to most but seeing the math of "why" it is EV neutral might help.
Last edited by tuds38; 12-08-2017 at 04:36 PM.