Dice Game Strategy

I'm running dice rolling game in a forum. I wanted to see the basic strategy behind when to take the pot or roll:

Object
To have the most chips at the end of the game.

On Each Turn
One chip will be removed from the Bank and added to the Pot. The player will roll one four-sided die (1d4). If the player rolls a 1, he is "aced out." His turn is over and the next player begins his turn.

If the player does not roll a 1, he may either collect the Pot and end his turn, or he may roll again. If he rolls again, two chips will be removed from the Bank and the player will roll two four-sided dice. If he rolls a 1 on either die, he is "aced out." If he doesn't roll any 1's, he may take the pot or keep going with three dice.

This process continues, using one more die and adding one more chip each time you repeat. If the player ever rolls a 1, he is aced out, and if he doesn't roll a 1, he may either take the Pot or roll again. Whether he aces out or passes, the next player always starts again at one die. Anything left in the Pot remains for the next player to shoot for.

Winning
If the player makes it all the way to 5 dice and still doesn't ace out, he immediately wins the Pot and collects the remainder of the Bank. Otherwise, the game continues until the Bank is empty.

After the Bank is emptied, the winner is the player with the most chips.

to start, what is your strategy so far?

I have no strategy. I'm the one running it.

The strategy seems a bit more difficult, as I am always wagering the pot to win the pot. I have figured out my chances of not acing out on each turn, so I'm sure that's a start:

1 die: 75%
2 dice: 56%
3 dice: 42%
4 dice: 32%
5 dice: 24%

Other than that, I can't figure it out.

If the pot is empty when you start, your EVs are as follows:

1 dice = .75
2 dice = 1.256 -- (.75) * (.75^2) * 3
3 dice = 1.068 -- (.75) * (.75^2) * (.75^3) * 6
4 dice = .5631 -- (.75) * (.75^2) * (.75^3) * (.75^4) * 10
5 dice = .2673 -- (.75) * (.75^2) * (.75^3) * (.75^4) * (.75^5) * 15

If the pot is not empty when you start, you need to calculate when the expected value will be the highest.

If the pot has 2 or more units (before your roll), then it is advantageous to take the pot on the first roll (when the pot has 3 or more units).

Of course, you would adjust your strategy based on who is winning.

The strategy is dependent on 3 factors which would make a complete analysis very complicated:
a) size of current pot
b) size of the bank (since you can win it all on the 5th roll)
c) amounts you and the other players have already won.

Also, are there any prizes for coming in 2nd, etc? Or are you looking for a strategy to maximize your chance of winning?

At any decision point, you could calculate your EV for taking the pot vs. rolling, using a formula based on the size of the pot & the size of the bank ( I am casually working on a formula, maybe i post later). Choosing the higher EV would maximize your expected chip count.

But... knowing the amounts the other players had already won is important for deciding how to maximize the win. Near the end of the game your strategy would change depending on who was winning and by how much.


** edit - simulpost!**

My calculation then for 5 dice is wrong. You would try to get to all 5 dice when the pot + the bank is 94 units or more. At that point the EV would be greater than the 2 dice roll (with no pot).