The Schnapsen Log
All the Aces (appendix 1)
Martin Tompa
We want to count the number of hands Hans could hold that have at least one card in each suit, but not all four kings. In this case, he must hold 2 cards of some suit and 1 in each of the other suits. If his 2-card suit is ♣, then there are 7 hands he could be holding that satisfy all conditions: he could have either of 2 cards in each of the other 3 suits (that’s 2⋅2⋅2 = 8 possibilities) minus the one combination of all kings. There are 3 other possibilities for his 2-card suit; for each one, there are 2⋅2 - 1 = 3 hands he could hold that satisfy all conditions. (Remember, we do know he holds ♣K, because he showed the royal marriage.) In total, there are 7 + 3⋅3 = 16 hands that satisfy all conditions.
© 2012 Martin Tompa. All rights reserved.
