Dice game seen in a movie

[AndysDaddy]

I was watching a strange (by today's standards) movie last night called "Boys Night Out". I loved the movie, but that, and the plot of the movie are not relevant.

In one scene in the movie James Garner's character goes to pay his bar tab. He and the bar tender agree to "roll for it" - presumably double or nothing. As near as I can tell, here are the rules of the game:

- There are four six sided dice, which you roll to start the game
- You can choose to reroll some, none, or all the dice once (all at once).
- "Hands" are ranked as follows: 4 of a kind beats 3 of kind, beats two of kind, beats High Dice. The dice value of the quad, set, etc breaks a tie. Further ties are no action. Two pair, straights, and the value of non-paired (tripped, etc) do not count. Examples:
Four 6s beats everything (tying four 6s of couse)
Four 1s beats 3 6s
5-5-5-3 ties 5-5-5-6 : non paired dice do not count
5-5-4-3 beats 4-4-3-3 : No "two pair" hands
6-3-2-1 beats 5-4-3-2 : High dice-6, no straights
6-5-2-1 ties 6-4-3-2 : High dice, non "paired" dice do not count.

I hope that explanation is clear.

The scene was very brief, and I'm deducing the rules of the game to some degree. My first thought when I saw this scene was "Why would the bartender play this game?" I was thinking this was an EV-0 game, and perhaps its just for fun (knowing he'll break even in the long run), and the customers enjoy it.

Almost immediately afterward I realized that unless the customer plays the most effeicient strategy, the bartender can make this a +EV game by playing perfectly. A little while longer, I had the thought that by politely "allowing" the customer to always play first, he can increase his EV by playing perfectly for the target score.

My questions to you probability experts are these:
- What is the perfect strategy for maximizing your hand?
- Given a hand you must beat, how does this strategy change?
- Assume the customer plays this simple strategy:
* On the first roll, keep whatever you roll most of, keeping the higher dice on ties, and reroll the others.
- What is the bartender's EV?

Have fun
--
Scott

[Bostaevski]

They play something just like this in my home town except I've never seen it for the tab. Someone can "roll" for quarters to put in the jukebox (when there's no music playing). Basically the bar-fly gets to pick some free songs when he wins.