# Ordering up the upcard

## As 1st Hand

1st hand is placed in the unique situation that he is disadvantaged by not yet having received any input from any other player having already passed during bidding. But he is advantaged by the fact that he gets first lead.

To order up as 1st hand, his cards must be sufficiently strong to defeat his opponents, who by the fact that they have been ordered up, will now have an extra trump. It is worthy to note that if you have only 2 trump, then there is a 47.7% chance that at least one of your opponents already has exactly 2 trumps -- excluding the upcard. There is a 3.25% chance that both your opponents already have 2 trumps, which by inferrence, means both that the dealer will end up with three, and your partner will have zero.

If you have 2 trumps, what can you expect for trump distribution? There are 3 trumps accounted for, the dealer will end up with the upcard trump. So there are 4 trumps left. There are also only 17 positions for the 4 remaining trump. 3 positions in the kitty, 5 in each of 2nd hand, and 3rd hand, 4 in the dealer's hand. The following probabilities apply accounting for the upcard being in the dealer's hand:

1st Hand Having 2 Trump

 Location # of trump Probability Kitty 0 42.06% 1 45.88% 2 11.47% 3 0.59% 2nd Hand 0 20.80% 1 46.22% 2 27.73% 3 5.04% 4 0.21% Partner 0 20.80% 1 46.22% 2 27.73% 3 5.04% 4 0.21% Dealer 1 30.04% 2 48.07% 3 19.66% 4 2.18% 5 0.04%

1st Hand Having 3 Trump

 Location # of trump Probability Kitty 0 53.53% 1 40.15% 2 6.18% 3 0.15% 2nd Hand 0 32.35% 1 48.53% 2 17.65% 3 1.47% Partner 0 32.35% 1 48.53% 2 17.65% 3 1.47% Dealer 1 42.06% 2 45.88% 3 11.47% 4 0.59%

The probabilities are exclusive. That is, there is not a 75.80% (27.73% + 48.07%) chance that both 2nd hand and dealer will each have 2 trump. You can only ask questions about one player at a time. In any event, there is a 33% chance that the player to your left (who gets to play after you) has 2 or more trump. There is a 21.88% chance that the dealer will have more trump than you, and a 48% chance that he will have at least 2 -- which is a disadvantage if you want to lead trump. Because the dealer will play last, he will be in a good position to maximize a tenace holding in trump.

If you are certain of 2 trump tricks because you have both bowers, the risk is acceptable, since your partner has an equal chance of holding the top card in an offsuit. If, however you are highly expectant of both trump tricks because of a void, you still may not draw enough trump and risk losing one trump trick to each opponent by them trumping an offsuit.

It is reasonable to assume that if you have 3 trump, that the dealer has 2, and that both 2nd hand and partner each have no more than 1. So a reasonable course of play is to order up if your hand has other quality aspects and then immediately lead a high trump. The worst case scenario is that dealer wins and 2nd hand has an additional trump. In such a case, which is only only a 1 in 5 chance, you might be Euchred. My recommendations:
 If you hold Action Both bowers with opposite colour doubleton Ace/x Order up Both bowers with opposite colour singleton King Order up Both bowers with 2 Aces Order up Both bowers with any Ace and any 2 Kings Order up 3 Trump, 2 of which are King or higher Order up 3 Trump, with upcard showing 9 or 10 Order up 3 Trump, with 2 voids Order up 3 Trump, with opposite colour singleton Ace and void Order up 3 Trump, with 2 offsuit (singleton) Aces Order up 2 Trump, both Ace or higher, and an opposite colour singleton Ace Order up 2 Trump, both Ace or higher, and an Ace/King/x tripleton Order up 2 Trump, at least one of which is greater than the upcard, and 3 singleton Aces Order up