Anyone ever play the game 31?
 

Rules:

Each player is dealt 3 cards face down, discard/draw piles in middle. Each player has option to take face up card or draw and must discard after hand, like gin. Goal is to get highest total; cards are counted like blackjack but must be suited, with the exception that a set counts 30.5. AsTsTs = 31 wins instantly; all other hands must knock. Knocker lays 2:1 that he can beat at least one other player; each other player immediately following knock has one final turn to improve. Low hand loses.

Questions:

I'm struggling with the exact probabilities to find a) at what total one should knock first hand, dependent upon position [note that the 'UTG' player, upon knocking, would limit opps to one additional card each, while the 'button' player would face two chances - albeit only one where the opps knew the finite horizon] and b) what a reasonable rate of improvement would be over the course of several rounds of a hand [how quickly does a particular holding devalue?]

Any help, or just random thoughts, would be highly appreciated.

Cheers!

Re: Anyone ever play the game 31?
 

I calculated the average starting hand to be ~13.0
Given the chance to pick 1 additional card the average hand will improve to ~15.7

This was calculated through a sim.

Edit: Just noticed I didn't take into account the fact a set was 30.5... but I doubt that will change the numbers more than .1

Re: Anyone ever play the game 31?
 

I played it once. And that was years ago. I barely remember what the game is about even after reading you post.

Well, I guess my post wasn't helpful, but I did answer your title question.

Re: Anyone ever play the game 31?
 

Sim, eh? Where could I find one of those? Are they available in such a flavor as to input any opening number of cards and draws?

Also, note that the average hand might not be the important one as the knocker has to lay 2:1.

Re: Anyone ever play the game 31?
 

Usually, especially with off the path games like this, you have to write it yourself.

Maybe this tutorial will help.

Man, that was sarcastic... I'm sorry =D

Re: Anyone ever play the game 31?
 

i play a game called 13, or tien len. its the best.

Re: Anyone ever play the game 31?
 

har har.

No worries, I figured as much. Unfortunately, I haven't done any programming for a while, nor do I know any C++. Of course, the saddest thing of all is that I just finished a degree in economics from a top-10 program, with a year's worth of statistics and a healthy helping of game theory, and I still get stuck doing what should be relatively basic [censored] like this.

And I'm unemployed.

Che sera, eh? Time for law school.

Re: Anyone ever play the game 31?
 

Here is the "random thoughts" you were asking for...

I played a game called schwimmen (sp). Very similar

http://www.pagat.com/commerce/schwim.html