Need help with solving a sequence

[leo321]

Hello i would like to have some help with trying to figure out the following problem.
I would like to know of a equation or some kind of math generator if available to help me figure out a solution, or where I could find information on solving this problem.

The problem I have is kind of like a game:

Each game consists of 6 short rounds. In each round, you and your opponent will bid on 6 coins 1, 2, 3, 4, 5 or 6. At the start of each round, one of six coins will be randomly dropped on the middle of a scale with each coin appearing only once. You and your opponent will each have 6 coins of your own which you must risk during play.

Using your own coins 1 to 6 (where each coin can be used only once), you must try to outbid your opponent in order to tip the scale in your favor and win all the coins After 6 rounds, the player with the most coins wins the game.
For instance:

|----------------------------------------|
| Dealer's |  my  | opponent's |         |
|   coin   | coin |    coin    | outcome |
|----------------------------------------|
|     4    |   3  |     2      | I win   |
|     3    |   2  |     5      | I lose  |
|     2    |   1  |     4      | I lose  |
|     5    |   4  |     3      | I win   |
|     1    |   5  |     6      | I lose  |
|     6    |   6  |     1      | I win   |
|----------------------------------------|
| My Total:   34                         |
| Opponent's total:    29                |
|----------------------------------------|

Overall, I win the game.

I want to know which number to play for any random dealer coin played, to overall win the game. This is pretty complicated to me and I haven't been able to figure it out. I would greatly appreciate any help or info or guidance in the right direction. Thank you

 

[Denis]

Leo, you better explain that better...

Do you always play first?
Dealer coin=6; you play 6; can opponent play 6? if so, who wins?

To tell you the truth, game makes no sense...

 

[JakeD]

This looks to me like a dynamic programming problem, similar to this one but more complicated. May I ask the source of this problem?

 

[leo321]

Sorry about it being confusing, but its hard to explain. To answer your questions yes i go first, any number can be played but only once. Say dealer plays a 5, i can play a 5, and my opponent can play a 5. It is kind of like a betting game, but its a blind bet. And whoevers bet is higher each round wins the dealers coin plus your own coin and the opponents coin. After 6 rounds whoever has the highest amount wins the game. I want to know what number coin i should play for any round to overall win the game. There must be countless different possible ways the game can be played, and ways of winning. Say 6 rounds, 6 dealer coins, 6 of my own coins, and 6 opponent coins.
So 6x6x6x6= 1296 different ways the game can possibly be played. If im not mistaken. So how do i figure out how many winning possiblitys. And what are they. If its possible to figure? Thanks for wrapping your brains around this one.