Update 2: Chutes and Ladders
Well, I did the same analysis for chutes and ladders already.
The data ( In terms of the transition matrix, move data, and some of the graphs ) is here:
It was generated in a similar fashion to the data from Monopoly:
1. I created a transition matrix that determined the probability of reaching some space ( column ) from some other space ( row ). As there are many versions of Chutes and Ladders available, I modified one and used it for this analysis
2. I then created a move one scenario ( where you start on space 1 ) , and multiplied that matrix with the transitional matrix 200 or so times.
3. I finally analyzed what I got, and it was pretty cool!
To summarize, here are some of the interesting conclusions that can be drawn:
1. It takes precisely 12 moves for the 100 square to be the most probable square on the board ( with a 6% chance of winning this early )
2. It takes 28 moves for square 100 to have a 50% chance of being landed upon
3. The most probable square to land on, after square 100, is square 84 after 30 moves or so.
4. The series 1,3,8,11,6,42,26,26,26,44,44 describes the most common spaces to land on at moves 0,1,2,3,....
5. On average it takes about 21 moves to finish a game
Overall, Chutes and Ladders is a far easier game to describe than Monopoly, yet its random nature allows for some pretty clever phenomena, and demonstrate some of the weirdest things I have seen in a game of chance in a while.
The data ( In terms of the transition matrix, move data, and some of the graphs ) is here:
It was generated in a similar fashion to the data from Monopoly:
1. I created a transition matrix that determined the probability of reaching some space ( column ) from some other space ( row ). As there are many versions of Chutes and Ladders available, I modified one and used it for this analysis
2. I then created a move one scenario ( where you start on space 1 ) , and multiplied that matrix with the transitional matrix 200 or so times.
3. I finally analyzed what I got, and it was pretty cool!
To summarize, here are some of the interesting conclusions that can be drawn:
1. It takes precisely 12 moves for the 100 square to be the most probable square on the board ( with a 6% chance of winning this early )
2. It takes 28 moves for square 100 to have a 50% chance of being landed upon
3. The most probable square to land on, after square 100, is square 84 after 30 moves or so.
4. The series 1,3,8,11,6,42,26,26,26,44,44 describes the most common spaces to land on at moves 0,1,2,3,....
5. On average it takes about 21 moves to finish a game
Overall, Chutes and Ladders is a far easier game to describe than Monopoly, yet its random nature allows for some pretty clever phenomena, and demonstrate some of the weirdest things I have seen in a game of chance in a while.
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