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Would like to know what method, or distribution to use when solving a problem like this:

I start from level 0. There is a probability p chance to drop to level -1 and a (1-p) chance to increase to level 1.

The levels range from level -n to level n. When it reaches level -n or level n, it resets back to 0 on the same cycle.

(Also, if you are at level -1, there is (1-p) chance to go back to level 0)

How do I calculate the percentage of landing on each level (not counting the reset), assuming I continue running this infinitely? Seems like dependent events. Is there any theorem or formula I can use?

Thanks!

I start from level 0. There is a probability p chance to drop to level -1 and a (1-p) chance to increase to level 1.

The levels range from level -n to level n. When it reaches level -n or level n, it resets back to 0 on the same cycle.

(Also, if you are at level -1, there is (1-p) chance to go back to level 0)

How do I calculate the percentage of landing on each level (not counting the reset), assuming I continue running this infinitely? Seems like dependent events. Is there any theorem or formula I can use?

Thanks!

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