Wizard (card Game) - First Hand Probabilities

First Hand Probabilities

Since there are no options for which card to play when you are only holding one card, there is a statistically correct bid for any given card. Note: This only truly applies if you have the lead, and thus no information from other bids. Since a correct bid of 1 yields 30 points, and a correct bid of 0 only yields 20, a bid of 1 over time yields more points as long as you have at least a 42.86% chance of winning the trick.

The known cards are only your own card and the turn up, so with 58 unknowns, the odds your hand will win in a 3 player game are calculated by the odds that both of the other hands lose to you. That is, (x/58)*((x-1)/57), x=# of cards you can beat. The calculation is similar for more players. Solving for x to yield 0.4286 or greater gives the minimum number of cards you need to be ahead of to justify a bid of 1.

With the lead:

• In a 3 person game, x=39, bid 1 with an offsuit Jack or stronger.
• In a 4 person game, x=44, bid 1 with the 3 of trump or stronger, (4 of trump if the turn up is the 2 or 3).
• In a 5 person game, x=49, bid 1 with the 9 of trump or better, (the 8 will do if the turn up is higher than the 8)
• In a 6 person game, x=50, bid 1 with the 10 of trump or better (9 if turn-up is 10 or higher)
• In the special case that a jester turns up and there is therefore no trump, and you have the lead: always bid 1 in a 3 player game, With 4 - bid 1 on 3 or higher, with 5 - bid 1 with any 9 or higher, and with 6 players a 10 or higher.