Peter Hallberg
World Backgammon Champion 2004

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January 2011

The fear of letting go

Mar 7th by Peter Hallberg

We cling to our beliefs and we cling to the best
explanations we have for things
no matter how weak they are
but we dare not let go

The intro ended up sounding almost religious. However, as you know I'm from Denmark and we as a population have one of the highest proportions of atheists and agnostics and I belong to that group as well. Be clear that I don't reject god or think bad about people that do embrace religion - that's their personal choice. In the name of reason, I just simply can't give into the idea of a personal god. In my opinion a god simply isn't the best guide in our daily lives and god isn't an explanation for things we don't (or won't) understand.

No matter how much I think my life is governed by facts and reason, I often find myself lost to thinking that 'someone/something' is testing me when the negative variance in games hits me harder than a being hit by a runaway train. At those times I feel like abandoning rational thinking and succumb to the idea that I'm not in control of my destiny and I'm only a piece of a bigger plan.

That's a really strange feeling and I wonder what it is, certain games have, that would make me experience/feel things, that is not present in any other part of my life.

This is a two part blog where I will dig into the perception of luck in poker along with variance and superstition.

Perception of luck in poker
Luck is difficult to quantify in most games. This goes at least as much for poker as for any other game. Everybody talks about allin EV if that was the 'right' way to measure luck. It does indeed tell us something about how good or bad we're running, after the last dollar went into the pot - but that's all. It's doesn't tell us if it was a setup hand or if the hand was played good or bad. We don't even get credit for getting 90% of the money in good and the last 10% in bad.

Take a situation where you are dealt KK ten times and get all the money in pre-flop against AA. You win half of them. It was quite unlucky to get into this setup but it was lucky to suck out three time more than the odds dictate. In my view the luck canceled out and both players got exactly their EV measured before the hands were dealt.

There are other ways to tell if a player is lucky. In a 6-max cash game it is generally recognized that it's really unlikely for a player to have a win rate of more than 10 big blinds per 100 hands (bb/100) in the long run. When a player has a higher win rate, say 20 bb/100, we understand that he had to be lucky to win this much even if he is one of the best players. In this case it's easy to recognize that the player in question was lucky.

Say a player is losing 20 bb/100. We know it's possible for a big fish to have such a bad win rate. This time we can't say anything about luck based on the win rate alone.

As poker players we hear all kinds of stories from our peers. If you take 100 players that know of each other and ask them if they think they are among the ten best players of the group, you would most likely get 25 players in the top ten. The same principle apply to the case of how unlucky players think they are. There are at least 25 players (probably even more) who think they are among the unluckiest ten.

Because it's really hard to objectively tell if a player is unlucky or just plain bad we don't give anyone the benefit of the doubt. We assume that they are doing something wrong. Well, that is partly right because everybody does something wrong, but that doesn't have to result in a bad win rate. Let's get this clear. There are infact 10% players that are among the 10% unluckiest players. Somebody has to do the dirty job.

But how bad can you run?

The variance beast
It is common knowledge that the luck will even out over the 'long run'. The question remains - How long is the long run?

Say, our hero play 3 tables at a rate of 100 hands per hour. He plays for four hours every weekday and take the weekend off. After two month he would have played approximately 50K hands. This can definitely feel like a long time, especially if you are running bad.

If you are a good player and have a true win rate of 5 big blinds per 100 hands, what are the chances that you lost money over this two month period? It would seem like almost impossible to not win money over this sample of hands but unfortunately it's far from true.

I've used a variance simulator to create the following two graphs. The parameters for the simulator are:
Presumed win rate = 5 bb/100: This is the win rate we objectively think our player can uphold.
Standard deviation = 90 bb/100: How big are the swings given our players play style. I have used my SD taken from Holdem manager.
Number of hands = 50.000: Taken from the example.
Number of runs = 1.000: The biggest sample size possible in the simulator.

Looking at the first graph we see that the unluckiest player (blue line) with our heros stats will end up losing more than 4000 bb over the 50K hands! Had there been no variance he would have won 2500 bb. That's crazy but then again this was the most unlucky one of the 1000 runs.

Take a look at the second graph. The area under the graph from 0 and down represents the portion of runs that lost money over the 50K hands. That's a significant part. I don't have the exact number, but it looks like about 10%!

In the next blog I take a look at some of the consequences it might have to run bad.

Read part 2 here.

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