Hearts or Clubs? Why the AI gives the weaker trumps the better chance

You pick up the skat and hold two Jacks, the Ace and Ten of Clubs and four Clubs in all. Clubs is the obvious game. Yet SkatGo's win chances say Hearts: 97% for Hearts, 87% for Clubs. Here is why the AI likes the game with the weaker trumps better, and what that teaches about choosing a game.

The hand

You sit in rear hand, the bidding stopped at 18, and after picking up the skat you hold these twelve cards:

You put away ♠7 and ♥7. That leaves you void in Spades, whatever you play.

Clubs: good trumps, a weak side suit

• Your trumps: ♣J ♦J ♣A ♣10 ♣8 ♣7. Six trumps, with the Ace and Ten of trumps. That looks like a safe game.
• Your side cards: ♥K ♥9 ♥8 and ♦A.
• The problem is Hearts. The opponents hold ♥A ♥10 ♥Q. Your three Hearts are losers: when Hearts are played, the opponents take those tricks, and their Ace and Ten bring 21 card points home. Your ♥K can easily fall with them.

Six trumps are worth a lot, but they cannot stop three Heart tricks going the wrong way.

Hearts: weaker trumps, side cards that score

• Your trumps: ♣J ♦J ♥K ♥9 ♥8. Only five, and the opponents hold ♥A and ♥10. That is the weak point of this game.
• Your side cards: ♣A ♣10 ♣8 ♣7 and ♦A.
• Your weakest suit is gone. The small Hearts that lose tricks in a Clubs game are trumps now. They can win tricks instead of giving them away.
• Your strongest cards bring points home. ♣A and ♦A win their tricks at once. Once ♣A is out, ♣10 stands too. The opponents hold only three Clubs between them (♣K ♣Q ♣9), so your Ace and Ten are likely to make it before anyone can trump them. That is 32 card points from three cards.

So the choice is between good trumps with three losing Hearts, and weaker trumps with no losing suit and three strong side cards. The AI rates the second higher: 97% against 87%.

Is that a bug?

We checked. We exchanged Clubs and Hearts in the hand (the Jacks stay as they are) and asked again. The two numbers exchanged too: Clubs 97%, Hearts 87%. The chances follow the cards, not the name of the suit.

Putting away ♥7, which is a trump in a Hearts game, costs almost nothing here: with the AI's own best two put away, Hearts is 98%.

What to take from it

• Don't count only your trumps. Count your losers too. A suit of small cards without the Ace is where tricks and points go to the opponents.
• Look at which game makes your weak suit trump. Turning three losing cards into trumps can be worth more than holding the Ace and Ten of trumps.
• Side Aces and Tens are points you bring home. In a suit game they win their tricks early, before the opponents are void.
• Both games cover 18. Clubs "with 1" is worth 24, Hearts "with 1" is worth 20. Clubs is worth more, but Hearts is more likely to be won, and a game you win counts more than a bigger one you lose.

Try it yourself

In free play, the lightbulb on the left of the table shows the win chances for every game. While you bid, they are worked out over every skat you could find. After you pick up the skat, they are for the skat you found. Select two cards to put away and open it again: the chances change with the two you chose.

Limits

• The chances are the estimate of SkatGo's AI (SkatZero) from many games it played against itself. They are not a guarantee, and a person may play the hand differently.
• This is one hand. In most hands the longest trump suit is also the best game. The point is to check, not to assume.