I have read a ton of posts about this , I know it is 0Ev and just a way to reduce variance.

But assuming you are a mortal winning live pro playing less than 100k hands a year, wouldn't it make sense to try to reduce variance when we are ahead and to keep it higher when we are behind?

Hello DelusionslFish,

0EV variance should be avoided, if possible, wether or not we are ahead or behind.

Some famous pro players never run it twice, some always want to run it twice, and the majority are a mix of the two.

Phil Ivey and Barry Greenstein come to mind when I think of pros who choose to run it once, almost exclusively.

So, why would two of the best cash players always choose to embrace variance for no apparent reason?

Ivey has talked about how he plays high stakes poker. With regard to swings, he states that he really enjoys the game and plays best when the money at risk becomes large enough to make him sort of nervous (I am paraphrasing, these are not his exact words). This is a person who is practicing the elimination of irrational fear of losing. Whatever the decisions were made before all the money goes in, Phil Ivey will embrace the winning or losing without fear, or at least without the slightest outward sign of it. Quite astounding, I really can not imagine that level of discipline. This all adds to the mystique of Phil Ivey.

As for Barry, I'm sure he has written about it somewhere, but I just cant remember it. He has talked some strategy from time to time.
My guess, totally from just his general description of poker, is that his level of discipline is generally higher than the opponents that he prefers to play against. If a weaker player wins a big hand, they are more likely to donk it off later, while if they lose a big hand they are more likely to tilt and rebuy. Barry is immune to all if this and plays the same regardless. So, bigger swings do nothing to him but potentially weaken his opponents.

So, there are at least two different perspectives on the matter and I am sure there are plenty more reasons to run it once.

Running it twice is generally considered a courtesy among players who view each other as relative equals.

Most of this reasoning is not optimal behavior, by the way. Pros should want to knock each other out of the game by running it once, and keep fish in the game by running it 3,4,5 times etc.

This is confusing me more, shouldn't we be indifferent about it?

No, lower variance is better. Would you be willing to risk your whole bankroll on a 50.1% to win? You shouldn't be.

Greenstein has stated he never runs it twice because it gives him a psychological advantage. Since opponents know he will not run it twice they will be risking their stack on one run and therefore may not want to take the risk. Apparently Barry feels this advantage outweighs the reduced variance RIT gives him.

Sorry, I am particularly long winded and stray far from the actual question asked, from time to time.

You should be indifferent to winning or losing any particular hand of poker, regardless of whether you are up or down.

However, running it twice has nothing to do with winning, as you correctly volunteered up front in your original post.

When every possible factor is equal between both decisions, thus truly 0EV, then you should want less variance.

Unless....

There are always "unless" scenarios in poker theory which is why I gave a couple of examples of highly respected poker players embracing variance.

Read about the Kelly Criterion... And then imagine a situation where you either:
(a) win 10% of your bankroll 100% of the time (low variance)
(b) win 30% of your bankroll 50% of the time, lose 10% of your bankroll 50% of the time (high variance)

Same EV, but rate of growth is better for (a). Here's how to show that...

In the first case (a), you can consider your bankroll after a number of bets to look like the following, if you start with $1.
BR = 1 * 1.1 * 1.1 * 1.1... (As many 1.1s as bets are made)

In the second case (b), it would look something like this:
BR = 1 * 1.3 * 0.9 * 0.9 * 1.3 * 1.3 * 1.3 * 0.9 * 0.9...

But in the long run, each of the 1.3 and 0.9 terms will average out to sqrt(1.3 * 0.9) = 1.082

So in the first case, we are growing our bankroll by 10% every time a bet's made. In the second case, we are growing our bankroll only by about 8.2%.

Now, suppose instead we are on the losing end:
(a) We lose 10% of our bankroll every time a bet is made
(b) We lose 30% of our bankroll 50% of the time, and win 10% of our bankroll 50% of the time.

Again, both (a) and (b) have same EV, but (a) shrinks our bankroll slower than (b). And here's why:

Like before we have for (a)
BR = 1 * 0.9 * 0.9 * 0.9... [as many bets are made]

And for (b) we have something like
BR = 1 * 0.7 * 1.1 * 1.1 * 0.7 *...

And the 0.7 and 1.1 terms average out to:
sqrt(0.7 * 1.1) = 0.877

So in case (a) we are shrinking our bankroll by about 10% per bet, but in case (b) we are shrinking it by about 12.3% per bet.

tldr; Rate of growth of our bankroll will always be worse when we increase variance - whether we are on the winning or losing end of a bet.

Maybe there are better resources, but here's one:
http://www.elem.com/~btilly/kelly-criterion/

One other thing to mention... If our opponent's bankroll is smaler than ours, then it may be good strategy to tell them before hand that we always run it once - they will then be forced to take lower variance (at the loss of EV) lines against us, which could give us an advantage... I believe this is the reason players like Phil Ivey always run it once.

I know I've seen Ivey run it more than once on shows before, and I haven't seen Greenstein play in a while.

Honestly running it once just seems like something players do to make them seem tough being unphased by the variance. I can see the argument for how that might scare opponents into nitty play at nosebleeds in previous years but I don't think it really applies to regular cash games in 2017.

It just seems far superior to reduce your own variance and have a friendlier atmosphere for the recreational players.

Thank you very much. So, to make sure i understand it: Ahead or behind, the expected growth long term will be the same but with more variance it will take longer to be realised and this will always be to the detriment of our bankroll.

That 'psychological advantage' didn't work out too well when he lost a flip for $600,000 vs Esfandiari and effectively went busto. Antonio took his winnings and went on to win the One Drop. Barry had to become a playmoney reg. If he'd run it twice, Barry might still be playing high rollers. In addition, Barry reportedly had 100% of his own action on HSP, whereas just about all the other pros sold/swapped pieces.
QUOTE: "At that point, it was the biggest hand Antonio had ever won in his life, while for me, it was the one that really did me in on High Stakes Poker," lamented Greenstein. "I haven’t played a high roller event since I lost that pot, whereas it really turned Antonio around. He did really well that session and started playing high roller and super high roller events shortly thereafter."

No if EV remains constant, but variance increases, then expected growth is *worse*, when we consider growth to be the average proportional change to our bankroll.

Consider the example where you start with $1000 and flip a coin for half your bankroll. Heads you win, tails you lose.

Heads we win $500 and now have $1500
Tails we lose $500 and now have $500
Our EV is $0.

But..
Heads we win 50% and now have 150% our original bankroll.
Tails we lose 50% and now have 50% of our original bankroll.
The average growth of our bankroll is sqrt (1.5 * 0.5) = 0.866.

Even though our EV is $0, on average, at each flip we reduce the size of our bankroll by 13.4%.

Or you can think about it this way... Say we win one, then lose one. We'll have 1.5 * 0.5 = 75% our original bankroll. Same if we lose one then win one, we'll end up with 75% of our original bankroll. So on average, every two flips, we've lost 25% of our bankroll.

If you ran a simulation flipping coins for half your bankroll, you'll find you've soon gone broke. You'll eventually go broke flipping coins for any constant percentage of your bankroll.

Another way to look at this is that when we lose a coin flip, we lose a greater amount of utility with our bankroll than we gain when we win a coin flip.

So again to see if i understand:


To reduce variance here we could add a 3rd side to the coin where 33% of the time we dont lose or win anything and this would improve our growth rate.

Or maybe to reduce variance what we should do is bet a smaller % of our bankroll? this is what running it more than once acomplishes right?

25% of the time you win 50% of your bank
25% you lose 50%
25% you win 25%
25% you lose 25%

Betting a smaller % of our bankroll means playing in smaller stakes games.. And yeah, doing so would obviously reduce variance (in terms of $$/hour, not necessarily BBs/hour). But it also might reduce EV... That's why you should always be looking for a happy medium. Don't play too big so that you have a significant risk of going bust, but don't play so small so that you're unnecessarily giving up EV (if you're good enough for bigger games, and if they exist).

The stakes at which to play should also be informed by whether or not a player is practicing new skills, or simply "grinding". I like practicing new skills by dropping down to one stake above "JND". JND is "just noticeable difference" and is used by psychologists to differentiate between amounts (in this case) of money that a person actually cares about, and is subjective to that person. Also, we treat our poker money differently than our disposable income, even though they are actually all the same money (ignoring small losses in utility that come along with "making a deposit" etc.)

If you just don't care about five bucks, then don't practice at NL5. See if NL10 will get you to pay closer attention. If you can not remain focused at stakes that are within the recommended bankroll management parameters then you have other problems that need to be addressed and fixing those will greatly improve your game as well.

Since there are not so many stakes to choose from, it is simpler to just drop one level and practice additional lines that you have studied off the table. Once you are able to implement the way you intended, then go back to your grinding stake level.