Peter Hallberg
World Backgammon Champion 2004

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February 2011

Science geek at your service

Feb 15th by Peter Hallberg

It is very difficult for a group to make a decision that
involve a member to vote against his own best
for the benefit of the whole group

Today I have to examples of decision making that, in the moment, were very difficult but could have been solved but science.

Split or steal?
The rules are very simple:
You have a jackpot you play for. In the following example it's more than £100.000.
You have to choose split or steal and you opponent does the same without knowing each others choice.
If you both chose split you will split the jackpot and go home with £50.000 each.
If you both chose steal you will go home with nothing.
If one chose split and the other chose steal the person ho chose steal will take home all £100.000.

Let's watch this clip:

This problem is called the prisoner's dilemma. Let's remove the feelings involved in the decision making and take a purely mathematical point of view.

There are two scenarios:
1) You choose split: If you opponent chooses split you win 50% pot. If he chooses steal you get nothing.
2) You choose steal: If you opponent chooses split you win 100% pot. If he chooses steal you get nothing.

Now, from your perspective the only reasonable option is to choose steal. You can't consider split because your opponent will also know that the only reasonable option is steal. This way all split or steal should end up as steal vs. steal and the game show wins. That's not sad or anything - that's simply the way the game show works.

Choosing seats
Sune and I are working at an office with eight other guys at the moment. At the end of this month we are relocating to a new location and now we have to find a (fair) system to get everyone to agree on a seating plan. As one of the guys said: 'Position is everything!'. We decided to do this as adults and argue until we ended up in a deadlock. Then we decided the tiebreaks with the luck of a die.

There were three seats that people in general didn't like. Good for me because I thought they were the three best seats. After endless discussion four people were going for the same group of seats. They ended up being assigned to seats by random. How could we have solved this problem in a mathematical way?

I suggested that the last four guys made a prioritized list of the remaining six possible seats, without knowing each others chooses. Then they would hand them to me and I would minimize their overall discomfort. This field is called combinatorial optimization.

The idea is to try every possible combination of seatings. A given seating have a discomfort score that are the sum of the priorities each person got. Now we simply choose the seating with the lowest   discomfort score, meaning that the group in total benefit the most. If there are more best discomfort scores we choose the one where the unluckiest person are screwed over the least.

In reality nobody wanted to hear about this solution and before I could explain it to them the dice were in the air.


The fear of letting go, part 2

Feb 8th by Peter Hallberg

Continued from 'The fear of letting go'.

Consequences of a bad run
It is clear that Hero's bankroll should be able to withstand both the loss and the living expenses over this two month period. If he is playing NL200 earning $5K a month on average (having $4K in expenses) he would have lost $8K+$4K+$4K = $16K over this two month downswing, had he been the unluckiest player. Say he had a 100 buyin bankroll (that's $20K) he would now have $4K left and pretty close to broke!

If he had been running bad equal to the 10% unluckiest player he would have earned $0 thus spending $8K from his bankroll to cover living expenses, leaving him with only $12K.

Losing a significant part of your bankroll can result in stepping down a level or two. Now it's even harder to earn to your living expenses plus building up your bankroll again.

These calculations really put into perspective how many buyins you need to play at a certain level to be able to withstand variance over a modest 'long run' of 50K hands.

Development as a player
Regarding your development as a player I believe the difference between running good or bad is huge. If you start out by running good it gives you more room to try a more relaxed bankroll management style. Being able to test moves more freely is a huge benefit in the long run because it is essential to get 'hands on' understanding of concepts. Confidence and trust in your abilities are extremely important to set a realistic pace for learning and training/playing. There's little chance you decide to move forward into new territory if you 'feel' your skill level is insufficient at your current level, regardless of your actual skill level.

Positive/negative reinforcement
From a mental point of view it is a lot easier to handle short term downswings and bad beats if you are ahead. It just feels like you pay a little back. If you on the other hand are running bad and get bad beated even more it's really difficult to stay focused and positive. You might even get to a point where you don't care for details anymore because you feel like they don't matter anyway. Welcome to the spiral of bad decisions.

Say you are trying to make some adjustments to you game and you continue to be running bad. It would then be almost impossible to know if the changes had the desired effect. You might even abandon your recent adjustment and try something else. This doesn't have to happen many times before you don't know what is up and down.

If things go well you're much more likely to be able to play more hours. While running good there will be a much larger proportion of the time you play where you play your A-game, which often leads to even more success.

As most poker players I get affected by these downswings and struggle to get out of it again. But what about when I'm running really good? Unfortunately there are no really good personal poker experiences I can share with you. Instead I can tell you about my sick backgammon upswing.

The white hat
I have black hair. It gets crazy hot in the sun and when you're in Monte Carlo in the summer to play the backgammon world championship there's a lot of sun. Two euros were spent on a white hat with  the Monaco logo on it.

The day before the tournament started a friend had borrowed the hat and he returned it just before the start of round 1. I decided to wear the hat during the match. It took like 20 minutes to win the match against a really strong player. Usually a match like this would take 2 to 3 hours. Needless to say I was above average lucky. There were time to take a nap before round two.

When I headed back to the tournament area for the second round I brought my hat. Already it kind of felt like a lucky hat. This match was over after an hour and a half, with the desired outcome.

The 'unlucky' dice
To play in the championship you need to buy registered dice. I got a set for €40. To test them I challenged a guy to roll highest die for €200. He won and I threw my dice in the bin! A friend of mine thought that it was crazy and that I was superstitious. Then I proposed that we could swap dice if he felt that it meant nothing at all and so we did.

Every match including the semi final were played with his dice and I won them all. He managed to lose in the first round with my old dice.

Even more superstition
When you first give in to a little superstition there are nothing to stop you from trying everything. I tested out how to make the hat peak perform and it was concluded by a very scientific test that I had to hold my hand exactly on the top of it when I needed to be extremely lucky. Breakfast were the same everyday and I walked the same route at the same time every morning.

Why not? I kept winning. In the spirit of Pascal's Wager why not give into the superstition. If it's actually working, I'm unstoppable and if it's not working I just look like a fool. Not the first time. Been there - done that.

I ended up winning the whole thing and I certainly took the superstition to another level. The hat and the dice were locked in a safe at all times when not in use.

That's just crazy talk! It makes no sense... or does it?

The fear of letting go
Despite my general world view, where there are no room for superstition, I seem to abandon it all when it comes to poker and backgammon. It feels strange. Let me try to explain how I look at it.

My daily life
I'm really into science. It's so clear and as objective as anything can be. Science is build upon gathering facts and proposing theories that explains how facts are linked together. One of the most basic properties of a scientific theory is that it can be tested by experiments and that there exists an experiment that can falsify it. If more theories explains the same facts you simply choose the most well founded. A fantastic result of these theories is that they have some predictive value. For example the theory of gravity is well understood and we can predict a lot of things based on that.

Most decisions in my daily life is based on my understanding of how the world works. We all have small theories about how everything works. The better understanding we have and the more objective we can look upon a problem, the better we can solve it.

Here is one of my favorite examples. The traffic. We are driving on a three lane high way and we want to change lane. We look for a clear spot, turn on the turn signal and start maneuvering the car into the new lane. Three simple steps. Do that and you'll be okay. Unfortunately a lot of people start maneuvering before they turn on their turn signal. They either don't understand it or they just don't care. Say, we overlooked a car in the lane next to us. If we turned on the turn signal before we started maneuvering the car, the driver of the other car would have a chance understand our intention and react accordingly. Had we begun changing lane before signaling we would have ended up in an accident.

Understanding how things work enables you to stay out of a lot of trouble. I'm so wrapped up in this line of thought that it would kill me if I messed up due to acting without understanding. This is one side of the fear of letting go.

Poker and backgammon
Chance and variance is a big part of both poker and backgammon. My decision making over the board is based on the same principals as my daily life. I feel powerless against the variance beast and I'm willing to cling to anything when it rears it ugly face. During my time studying computer science I took some statistics and probability classes. I understand it quite well. It's still very hard to embrace the variance without letting it eat you up.

Games like poker and backgammon are activities done in time frames up to at most a week. Being lucky/unlucky has a much bigger effect on the outcome because there's only a short time span available to turn the tables around. Rolling that lucky roll or getting that unlucky card on the river will have huge impact on short time results. Believing that you might be able to affect the outcome through superstition can actually be a comfort in the moment. After the game it's clear that hoping for something doesn't make it come true. Yet, next time in the same situation I sit there with my lucky hat and hope for the miracle 66 to pop out op my dice cup. The fear of letting go is the fear of missing out if there indeed were ways to affect the outcome.

I hope I have many years in-front of me and that is probably why I do believe that luck will even out over time. That way it's easy to make the rational choices and optimize for longtime success. No matter how I look at it I'm not able to relax the standards of the rules I live by. If I did - where would I end? In between? That doesn't seem like a place I want to be...


:: Backgammon ::

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* Pokernyhederne (DK)

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