[EDIT] Sorry, KI in the title means actually AI.
I have to program an AI until next week for a little game and while I certainly not want you to do my homework I post it here because I think it's a pretty interesting problem and since I'm still oblivious to game theorie I'd like to get some inspiration for my approach.
The rules are as following:
Both players get n coins worth 1 to n and play for n cards with the same numbers on them (1,2,...,n). Each round they play for a random card, the one who puts a higher coin gets the card and both stakes get taken out of the game.
In the first round the beginner (to set) is chosen randomly after that the winner of the last rounds card has to begin. The one who sets first wins a draw.
In the end the one with the highest sum of card numbers wins (meaning there are (n+1)n/2 points to get in this game).
I hope the rules are clear, if not feel free to ask.
I still have to do some math before I can spell my first approach out, but in short it's about measuring the relative worth of a card (which is more than linear higher as the number gets closer to n) for both players (according to what points they made and who of them has the most dominant coins left) and set accordingly.
Game theorie / KI
Yes, it seems like the problem is mostly about remembering which cards and coins have been played and reacting accordingly.
A couple of other notions:
-For the first several rounds of play, it would seem generally unwise to make a bid higher than the value of the current card.
-The higher the value of the card, the more sacrifice is worthwhile to obtain it. Maybe start with increasing the bid for the top 50% of cards, and then scaling it according to whatever function you decide on for the value of the cards (and the number of rounds remaining).
-The problem is quite different depending on whether the AI goes first or not. Inherently, though, the player who goes first has a +1 value to their coins for that round. If the value of the card is low, it makes sense to intentionally lose the round to preserve this advantage.
A couple of other notions:
-For the first several rounds of play, it would seem generally unwise to make a bid higher than the value of the current card.
-The higher the value of the card, the more sacrifice is worthwhile to obtain it. Maybe start with increasing the bid for the top 50% of cards, and then scaling it according to whatever function you decide on for the value of the cards (and the number of rounds remaining).
-The problem is quite different depending on whether the AI goes first or not. Inherently, though, the player who goes first has a +1 value to their coins for that round. If the value of the card is low, it makes sense to intentionally lose the round to preserve this advantage.
We here shall not rest until we have made a drawing-room of your shaft, and if you do not all finally go down to your doom in patent-leather shoes, then you shall not go at all.