repost of a thread from pokerroad forums

people want to know when you should run it twice.
arguments are
hard to lose twice
can still win once
odds are the same each time

the first two make sense only in a "we are risking alot of money" sense
the odds are the same each time is true enough but you will be playing two pots instead of one. two smaller pots. what does that mean? well nothing if you look at the odds of winning each. but what it really means is that you increase the odds of a split. running it twice increases the odds of a split. so would you rather have the chance of a split increase when you are ahead or an under dog? only run it twice when you are behind.

i'd like to hear any pros opinions on this

also i solved the problem of the optimum bluff

This has been discussed. Numerous times. Running it twice doesn't change the expected value, but it lowers the variance. So run it twice if you want a lower variance.

yeah but lower variance or higher variance is a choice you can make depending on what you are prepared for.

in this situation its weird not wanting the odds of a split to increase when you are behind.

mines simpler

If you don't care about variance, then why do you care if you increase your odds of a split or not? If you do care about variance, that's the shortest answer for why you want to run it twice.

It's really only an issue for people who have more on the table than they're prepared to lose. If you are adequately backed, then you can take whichever road you choose. Losing full stacks is hard on the psyche for a lot of people and if losing this hand with a big favorite is going to make you tilt off more $ in the rest of the session then by all means reduce your variance, take it easy.

Of course, any steps you take to reduce your variance also effectively let you play in larger games because your effective required bankroll for a game is partly determined by your overall variance.

Anyway, there's nothing solved here because there's nothing to solve.

variance means the swings will either be big or small. swinging big or small doesent matter as long as you are making money. people can grind slowly or go on a rollercoaster.

but when you are behind and you don't want the chance of a split to be better you are probably doing something mathmatically wrong


so you can not care about variance but think of the fact you aren't making a correct choice at each turn. thats how your first sentence can happen

No. As we said before it doesn't effect your EV. Bear in mind that when you're behind and you run it twice, you severely reduce your chances to suck out.

so when i am like 20% to win or tie and i make myself 40% to win or tie thats not a good thing?

It gives you a 32% chance to tie, and only like a 4% chance to win outright. You've reduced your winning chances substantially.

EV wise, it's neutral

Variance wise, running it twice reduces variance. And yes this DOES matter, because the "correct" bankroll size for a given game is dependent on 3 factors:
risk of ruin tolerance
win rate
variance

if you decrease your variance in a way that does not effect EV, then you can play with a smaller bankroll, without increasing your chances of going broke.

you asked a question about a person who thinks it doesent matter. i answered. then the next post you tell me it DOES matter like I didn't know that.

also since we have this choice between high and low variance, why are we not choosing low variance when we are losing?

I'm gonna go out on a limb and say that this is a troll.

Saying you want to split more and win less is equivalent to saying you want low variance. I don't get what you're after here? A way to convince someone to run it twice who claims he doesn't care about variance?

Low variance is good, whether we're ahead, or we're behind. Do you see why?

One reason you might choose to run it twice if you're way ahead is if it would make you feel good to win a big pot right now. This is a short term / high variance approach but if that's what you want, I don't have any problem with it.

First off, I don't know what a troll is. I don't know what that means about anything.

if you are an 80% favorite for a big pot thats what you want to be.
the underdog wants to play two small pots which will increase his chance of a split. he wants low variance.

so basically when you are way ahead and that guy says "lets increase variance!" you say, "sure, i hope this works out for me"

Before we go any further, you do agree that in the long run it makes no difference for the person who is ahead. Right? The expected return from running it once or twice is the same?

(A troll refers to someone who is deliberately trying to make people angry or frustrated. I don't believe OP is a troll, he just has a different viewpoint on this

For historical reference, the word troll comes not from ugly creatures that live under a bridge. It's a fishing term where you cast out a line and cruise along slowly in a boat trying to get a fish to bite. Internet trolls do the same thing, they throw out a tantalizing bit of bait that you can't help but respond to, they enjoy creating controversy on their behalf)

yeah. can we disregard your facts about variance on a bankroll then?

i did the math the way everyone else was doing it based on effects on bankroll and stuff.
it may be the same in the long run but its kind of a disservice to not point out that alot of the time with small bankrolls you want low variance.

No. Lowering variance and keeping EV the same means you can play with a smaller bankroll.

so its equal in the long run but we have small bankrolls to worry about. so we have to choose the low variance option like i said. even pros have to worry about bankrolls not being enough.

before we get in a tizzy, i said we have to choose the low variance option cause of our bank rolls. im just telling you to do it when you are behind cause thats where variance happens. there's not alot of variance when you are an 70-99% favorite

Of course, if you want to minimize your variance that's an excellent choice. But choosing to run it twice minimizes variance for BOTH players, the one who is ahead and the one who is behind.

The player who is ahead as as much of a reason, bankroll wise, to choose to run it twice as the player who is behind.

The reduction to variance is the same, regardless of whether you're ahead or behind. Variance is upswings as well as downswings. (Keep in mind that by running it twice, the player who is an 80% favorite reduces his chances of losing the whole pot from 20% to 4%!)

noooooooo!
when you are ahead keep your 9 to 1 advantage (OR 6 to 1 OR 3 to 1 OR whatever)
it will work out for you! i promise.

Show me the math.

The expectation is the same no matter how many times you decide to run it. The variance of running it twice is always a little less than one-half the variance of running it once.

http://forumserver.twoplustwo.com/15...stions-316554/

You may prefer David Sklansky's "rigorous" explanation over mine.

http://forumserver.twoplustwo.com/25...2/#post6621159

ok jayshark. math same. we are you using logic to protect our bankrolls.


now for the math. if you continually take 3-1 shots as the favorite, eventually you will come out a winner. sometimes they win a few (bad Beats) but eventually you will come out a winner. thats how casinos do it.

...





Ha joking. I can't show you the math off the top of my head. I got to go play for the night. but i know its right.


if anyone wants to do us a favor and check the math of what happens when you only run it twice when you are behind and only run it once when you are ahead. be my guest

i'll try and get more math later

also check my optimum bluff thread.
did sklansky show you what happens if you do each every time and not the middle one where you do one in one situation and a different one in another situation?

that guys always doing


its like saying do this everytime and see what happens
now do the other everytime and see what happens
they're the same except for variance

I think doing one in a situation and another in a different situation will make it far more profitable

twice when behind. once when you are ahead

Really, you're demonstrably wrong here. If you can't do the math, get out excel and try it out. Take this, for example, it's pretty easy.

Let's take this over 100 trials. You the hero are a 4:1 favorite and I the villain am a 4:1 dog. Since this is a thought experiment, let's assume that the actual results match expected results exactly.

Run it once:
80 times you win 1
20 times you lose 1
expected outcome after 100 trials: 60
standard deviation: 0.80

Run it twice
64 times you win 1
32 times you win 0
4 times you lose 1
expected outcome after 100 trials: 60
standard deviation: 0.56

Do you see how it comes out *exactly the same* in terms of profit? But with lower standard deviation? So how could running it once be better? You're going to have to show me some proof (good luck!)



I'm pretty sure you're wrong about the optimal bluffing thing also, but I haven't actually sat down and taken time to work it out.

[ ] running it twice SOLVED