Solution of Septica

The game of Septica can be broken down into two subproblems:

  • finding a suitable strategy for the cases when you move first (this is also used by the computer);
  • finding a suitable strategy for the cases when the opponent moves first.

There are 2 possible situations for starting a trick:

  • Having at least 3 potential cuts in our set of cards (either valuable cards or 7s). In this situation, we start with a valuable card, because the chances of winning are high. Possible initial configurations (where X denotes any other card):
    • 10 10 10 10
    • 14 14 14 14
    • 10 10 10 X
    • 14 14 14 X
    • 10 10 7 X
    • 14 14 7 X
    • 10 7 7 X
    • 14 7 7 X
    • 7 7 7 X
    • 7 7 7 7
  • Having less than 3 cuts in our set of cards. In this situation, we start with a random card, provided it is not valuable (choose anything but 7, 10, 14).

There are also 2 possible situations of responding to a trick started by the computer:

  • The computer uses a valuable card (10 or 14) and we have at least 2 or 3 possible cuts in our hand. In this case, we can try to cut with a 7 or with the initial card used by the computer. If we don't have enough cuts, we use a random worthless card.
  • The computer uses a worthless card. We try to cut with either a 7 or with the computer's initial card.

All the heuristics described above provide a good enough strategy for our problem. The success rate of this solution is greater than 70% on random matches.

Questions?

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