Cribbage, for the uninitiated, like some variants of poker, involves choosing which card or cards to throw out to maximise the number of points you're likely to get. You can score points for your hand by having runs, combinations of cards that add up to 15 in value, pairs, three of a kind, four of a kind, flushes, and a strange one-point bonus named "one for his nob" <cough>
The variant of cribbage we'll work with here involves starting with 5 cards, and throwing one out. A single card, the "starter", is then chosen which acts as an extra card for your hand, replacing the one you discarded. Often you'll need to decide whether to take the risk and remove a card which might be useful in the hope that something better will come up as the starter.
Let's say you pick up this hand:
4♠ 4♣ 6♣ K♣ K♦
So, what do you do? All you know about are the cards that you picked up, and nothing about what the other player(s) might have. The starter could be any of the other 47 cards in the deck with equal probability.
If you discard a 4, you'll destroy one of the pairs, losing you 2 of the 4 points already in your hand. But if the starter comes up 5, it'll score you 11 points.
If you discard a K, you'll again destroy a pair. But again, if you pick up a 5, you'd score a tasty 14 points!
Finally, if you discard , you will have two pairs tucked away safely in your hand for 4 points. However, the best you can do from that point is get an A, which will get you 12 points.
By running through all 47 possible starter cards, we can work out (using the magic of computers!) every possible outcome of each choice.
|4♠ or 4♣||2||3.66||11|
|K♣ or K♦||2||4.26||14|
So if you're trying to get as many points as possible, your best option is to discard
And for discarding a K: