Difficult to evaluate, with potential yellow flags.
Unclear focus.
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I used Markov Chain analysis to assess Monopoly. My math worked flawlessly. However, I then proceeded to play a single game and dominate it to such an extent that I began to forgive rent simply so my friends would remain at the table by the end. This is a post about winning (optimizing), power, and what happens when a player knows he or she will ultimately win.
The Math
Monopoly is a discrete-time Markov Chain. Every space on the board represents a state; every transition is determined by a roll of the dice, as well as specific rules. If you calculate the stationary distribution, you will understand the long run probability of landing on each space.
The Results
The landing probabilities do not follow a uniform distribution. Jail is dominant. Illinois Avenue is the most-landed upon property. The lower left corner of the board experiences more traffic than anywhere else. Boardwalk is a trap. People may never land on it due to its high cost and rent. Properties 6-9 spaces away from jail, specifically those in orange, experience much more traffic for half the cost. Orange Dominates. Best Return on Investment in the game. All players who leave jail flow directly into orange.
The Game
I prioritized orange. I aggressively traded. I quickly built hotels. I had a complete monopoly over orange by mid-game. Neither of my opponents could ever catch up. As they continued to land on my properties and lose money, they eventually started putting their cards down. "That's okay," I said. "Don't worry about it." I waived the rent.
The Dilemma
It happened three more times. I would waive the rent when someone landed on my property, but I knew I wasn’t being generous. I was being desperate. The alternative was that I’d get rid of the competition (they’d quit) and I’d sit around with my perfect monopoly after “winning” a game that lasted 30 minutes and made everyone angry. I’d optimized so much that I became the game’s life support system.
The Coordination Problem
As we approached the end of the game, a friend asked if I wanted to make a trade for her remaining red property. She needed it to complete her set. I offered her a trade that gave us both monopolies. Both were positive expected value trades. However, the two friends looked at each other and said, “No. You’ve already won. We’re just trying to see who comes second.” They had coordinated. Instead of continuing to compete against each other, they began competing to limit my ability to win as quickly as possible. They traded with each other and excluded me from the trade. I still won – I had too big of an advantage. But they had changed the nature of the game.
The Meta-Realization
I wasn’t playing Monopoly. I was running it. I was managing everyone’s experience to ensure they stayed at the table.
I had optimized for: Winning this game I should have optimized for: Having a good time
The problem with total information dominance: Once your strategy is perfectly transparent, rational actors will organize against it. They cannot defeat the strategy, but they can defeat you — by playing a different game.
The problem with having too much power: When you are powerful enough that no rule constrains you, you need to constrain yourself. I became a welfare state not because I was generous — but because I had to be.
The problem with optimizing: I created a solved game. No one wants to play a game where the outcome is predetermined — even the winner. I didn’t enjoy playing the game either.
What This Shows
1. Optimization requires the right metrics The optimal strategy is not the one that creates the greatest chance of winning — it is the one that creates something of value. A sure thing that causes people to stop wanting to play the game is not optimal. Optimization occurs everywhere: being correct in arguments, min-maxing job performance, pricing products. The optimal local action often kills the necessary conditions for long term success.
2. Legibility has consequences My strategy was completely legible and completely dominant. Therefore, my friends organized against it. They could not overcome the strategy, but they could overcome me. There are times when you want to seem vulnerable. True power is winning while creating a system where winning matters.
3. Some games are best un-solved The joy was in the exploration, not the execution. Now that I know how it ends, what’s the point?
Conclusion The Markov Chain analysis was correct. Orange is indeed better than Boardwalk. The math worked. However, optimization without wisdom is nothing more than expensive foolishness. The game you think you are playing may not be the game that truly matters.
We are going to play again this coming Friday. Same friends, same board, same analysis running through my head. The true test isn’t whether I can win — it is whether I can lose on purpose and keep them from realizing it. That may be more difficult than the initial problem.
I used Markov Chain analysis to assess Monopoly. My math worked flawlessly. However, I then proceeded to play a single game and dominate it to such an extent that I began to forgive rent simply so my friends would remain at the table by the end.
This is a post about winning (optimizing), power, and what happens when a player knows he or she will ultimately win.
The Math
Monopoly is a discrete-time Markov Chain. Every space on the board represents a state; every transition is determined by a roll of the dice, as well as specific rules. If you calculate the stationary distribution, you will understand the long run probability of landing on each space.
The Results
The landing probabilities do not follow a uniform distribution. Jail is dominant. Illinois Avenue is the most-landed upon property. The lower left corner of the board experiences more traffic than anywhere else.
Boardwalk is a trap. People may never land on it due to its high cost and rent. Properties 6-9 spaces away from jail, specifically those in orange, experience much more traffic for half the cost.
Orange Dominates. Best Return on Investment in the game. All players who leave jail flow directly into orange.
The Game
I prioritized orange. I aggressively traded. I quickly built hotels.
I had a complete monopoly over orange by mid-game. Neither of my opponents could ever catch up. As they continued to land on my properties and lose money, they eventually started putting their cards down.
"That's okay," I said. "Don't worry about it."
I waived the rent.
The Dilemma
It happened three more times. I would waive the rent when someone landed on my property, but I knew I wasn’t being generous. I was being desperate. The alternative was that I’d get rid of the competition (they’d quit) and I’d sit around with my perfect monopoly after “winning” a game that lasted 30 minutes and made everyone angry. I’d optimized so much that I became the game’s life support system.
The Coordination Problem
As we approached the end of the game, a friend asked if I wanted to make a trade for her remaining red property. She needed it to complete her set. I offered her a trade that gave us both monopolies. Both were positive expected value trades.
However, the two friends looked at each other and said, “No. You’ve already won. We’re just trying to see who comes second.”
They had coordinated. Instead of continuing to compete against each other, they began competing to limit my ability to win as quickly as possible. They traded with each other and excluded me from the trade. I still won – I had too big of an advantage. But they had changed the nature of the game.
The Meta-Realization
I wasn’t playing Monopoly. I was running it. I was managing everyone’s experience to ensure they stayed at the table.
I had optimized for: Winning this game
I should have optimized for: Having a good time
The problem with total information dominance: Once your strategy is perfectly transparent, rational actors will organize against it. They cannot defeat the strategy, but they can defeat you — by playing a different game.
The problem with having too much power: When you are powerful enough that no rule constrains you, you need to constrain yourself. I became a welfare state not because I was generous — but because I had to be.
The problem with optimizing: I created a solved game. No one wants to play a game where the outcome is predetermined — even the winner. I didn’t enjoy playing the game either.
What This Shows
1. Optimization requires the right metrics
The optimal strategy is not the one that creates the greatest chance of winning — it is the one that creates something of value. A sure thing that causes people to stop wanting to play the game is not optimal.
Optimization occurs everywhere: being correct in arguments, min-maxing job performance, pricing products. The optimal local action often kills the necessary conditions for long term success.
2. Legibility has consequences
My strategy was completely legible and completely dominant. Therefore, my friends organized against it. They could not overcome the strategy, but they could overcome me.
There are times when you want to seem vulnerable. True power is winning while creating a system where winning matters.
3. Some games are best un-solved
The joy was in the exploration, not the execution. Now that I know how it ends, what’s the point?
Conclusion
The Markov Chain analysis was correct. Orange is indeed better than Boardwalk. The math worked.
However, optimization without wisdom is nothing more than expensive foolishness. The game you think you are playing may not be the game that truly matters.
We are going to play again this coming Friday. Same friends, same board, same analysis running through my head.
The true test isn’t whether I can win — it is whether I can lose on purpose and keep them from realizing it. That may be more difficult than the initial problem.
Let’s find out if I still got it.