Since there are no options for which card to play when a player is only holding one card, there is a statistically correct bid for any given card.
This only truly applies if a player has 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 the player has at least a 42.86% chance of winning the trick.
The known cards are only a player's own card and the turn up, so with 58 unknowns, the odds that a hand will win in a three player game are calculated
by the odds that both of the other hands lose to that player. That is, (x/58)*((x-1)/57), x=# of cards the player can beat. The calculation is similar
for more players. Solving for x to yield 0.4286 or greater gives the minimum number of cards a player needs 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 the player has 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.
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The First Hand Dilemma
There is a feeling that hand number 1 is problematic. In the 007 version, it is discarded completely. The reason given for this is that it is a
crapshoot. I do not agree. Certainly, your position is a factor. It is easier to bid last than first, but this is true for all bidding situations.
What do you know that will not make your bid simply luck? You know what card you hold in your hand. You know what is Trump. You know how many players
will bid after you. These 3 factors remove your bid from the 'crapshoot' category.
1. Your card: Holding either a Wizard or a Jester you know exactly what to bid. Holding a 10-J-Q-K-A of Trump you have to decide whether to bid 1 or
0.
2. What is Trump: Holding a card that is not trump you will bid zero. If it is a No-Trump hand you may want to bid 1 with an Ace or King.
3. Number of Players: There can be 5, 4, 3, or 2 bids after yours. The fewer the number of players the better your chances of winning with a high
trump card or an Ace or King in No Trump.
It is no Crapshoot!
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