I'm not quite sure if (any variation of) this question has been posted here. I could not find one.It is a two player game with a dealer. You, dealer, and your opponent each have 6 cards from 1 to 6. Every round, the dealer shows one of his cards (to both you and your opponent). Then, you basically "bet" on the card the dealer shows, with one of your cards in hand. Your opponent does the same. If your card is higher than your opponent's, you take the sum of the numbers on your card, dealer's card, and your opponent's card. For example, if the dealer shows 5, and you bet 4 and your opponent bets 3, then you get 5+4+3 = 12 points. Any cards used are discarded (so every round, you, dealer and your opponent have one less card to play with). If you and your opponent tie (i.e. betting the same card), then dealer's card, your card, and your opponent's card remain in the table, and the dealer shows another card on top of it. Then, you and your opponent bet again. It keeps on going until the tie is broken, and whoever wins the tie breaker wins the whole pile.For example, [dealer = 3, you = 4, your opponent = 4] (TIE) ==> [dealer 5, you = 6, your opponent = 5] ==> you get 27 points.The order of cards the dealer shows is random. Once you get 32 points, the game is stopped and you win (because there is only a total of 63 points available).My question is, is there any optimal strategy to (increase the chance to) win this game?

i don't know what the optimal strategy is, but the game above is a variant of so-called "Goofspiel".in the original version, winner only takes points from the deal's card, and there is a proof by Ross (1971) that the optimal strategy is simply randomizing if you have to bet before the dealer shows the card ("hidden card Goofspiel"). i would think the optimal strategy for this game should be along similar lines.

Oh, I did not know about it. Thank you.I just posted this game after watching my friend playing this game online and being asked by him of any optimal strategy.

For example, Sheldon Ross considered the case when one player plays his cards randomly, to determine the best strategy that the other player should use.[2] Using a proof by induction on the number of cards, Ross showed that the optimal strategy for the second (non-randomizing) player is to match the upturned card, i.e. if the upturned card is the Jack, he should play his Jack, etc. - from WikipediaExcellent! I could think of more or less the same strategy. Here is my answer:If dealer's card D happens to be greater than 3, I will bet my cards in the order 6,5,4, from high to low value, regardless of the actual value of D! The reason to do so is that these cards are quite worthy for me, so if my opponent wants to gain them I expect him to pay a higher price! So, in turn, he either adds to the value of the tie if he bets with the same card as mine (if he's following the same exact strategy) or he might throw a lower card if he has a different strategy. If the dealer's card D is ranked less than 4, then I will bet exactly the same as D. The reasoning is that I'm not interested in winning these cards as they are not very precious since the overall volume is low, but I also don't want to price the dealer's cards less than their face value. Moreover, I'm hoping that my opponent gets rid of his higher cards by paying more for the low cards which is not a good strategy any way. I think, if practiced correctly, this strategy can increase my chance of winning to a little bit more than 50% of the time if my opponents strategy has some random behavior, but to verify this, we should test the strategy with Monte Carlo..So in a sense I'm also matching with the dealer's cards, but I am further trying to bias my earning towards winning the higher ranked cards.