There are two players, A and B

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There are two players, A and B. At the beginning of the game, each starts with 4 coins, and there are 2 coins in the pot. A goes first, then B, then A,. . . . During a particular player's turn, the player tosses a 6-sided die. If the player rolls a:

• 1, then the player does nothing.

• 2: then the player takes all coins in the pot.

• 3: then the player takes half of the coins in the pot (rounded down).

• 4,5,6: then the player puts a coin in the pot.

A player loses (and the game is over) if they are unable to perform the task (i.e., if they have 0 coins and need to place one in the pot). We define a cycle as A and then B completing their turns. The exception is if a player goes out; that is the final cycle (but it still counts as the last cycle). We are trying to determine the expected number (and maybe even the distribution) of cycles the game will last for. I'm guessing that you can use"first-step" analysis to get the expected value.