### Expected Probabilities of Sets & Values of Cards

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**Sun Mar 18, 2007 12:59 am**The Double Whammy

A double whammy is when you wipe out another player and have so many cards that you have two mixed sets of cards to hand in. When you have a substantial number of cards as a result of wiping out an enemy (say, nine, because you had four and they had five) the probability of getting mixed sets goes way up. Even the probability of having two mixed sets is appreciable. Imagine you had 100 cards. About 33 would be cannon, 33 cavalry, and 33 artillery, so you?d have about 33 mixed sets. This synergy applies to smaller numbers of cards.

I worked out the probabilities of getting a ?double whammy? for the following amounts of cards, and the percent chance is the following.

6 cards: 12.4

7 cards: 28.8

8 cards: 44.8

9 cards: 42.0

(Note: this percent is approximate for nine cards, because it includes other ways of getting a value of 24, such as one mixed set, one set of artillery, and one set of canon.)

The chance of getting a ?triple whammy? when you have nine cards is 8.5% (not bad!).

The expected values of the armies from sets that will result from different numbers of cards in your hand are as follows:

3 cards: 3.3

4 cards: 7.3

5 cards: 9.7

6 cards: 13.2

7 cards: 17.2

8 cards: 20.0

9 cards: 23.6

(Note: these numbers are arrived at by multiplying the value of a set with the probability that you will get that set.)

A double whammy is when you wipe out another player and have so many cards that you have two mixed sets of cards to hand in. When you have a substantial number of cards as a result of wiping out an enemy (say, nine, because you had four and they had five) the probability of getting mixed sets goes way up. Even the probability of having two mixed sets is appreciable. Imagine you had 100 cards. About 33 would be cannon, 33 cavalry, and 33 artillery, so you?d have about 33 mixed sets. This synergy applies to smaller numbers of cards.

I worked out the probabilities of getting a ?double whammy? for the following amounts of cards, and the percent chance is the following.

6 cards: 12.4

7 cards: 28.8

8 cards: 44.8

9 cards: 42.0

(Note: this percent is approximate for nine cards, because it includes other ways of getting a value of 24, such as one mixed set, one set of artillery, and one set of canon.)

The chance of getting a ?triple whammy? when you have nine cards is 8.5% (not bad!).

The expected values of the armies from sets that will result from different numbers of cards in your hand are as follows:

3 cards: 3.3

4 cards: 7.3

5 cards: 9.7

6 cards: 13.2

7 cards: 17.2

8 cards: 20.0

9 cards: 23.6

(Note: these numbers are arrived at by multiplying the value of a set with the probability that you will get that set.)