Hints to Tyros
from "The Law and Practice of the Game of Euchre" by A. Professor -1862
When confident of winning two tricks, always assist and rely on your partner to win one trick.
The second player (the dealer's partner as they sit at the table) must remember, however, that when the trump card has been turned down by the dealer, and the eldest-hand has passed the making, it is his duty- though not quite so imperatively on him as it is on the eldest-hand to make the next in suit- to cross the suit, that is, to make the trump either of the black suits, (the one in which he is the stronger, of course) when a red suit has been turned down, and vice versa, and for nearly the same reasons, just given to the eldest-hand for making next in suit.
Part III
As second player rarely ruff a numerical lay card the first time round, as the chances are even that your partner may win the trick. Throw away any single lay card of less value than an Ace, if you have one or two small trumps, on such a lead, which will enable you to ruff its suit when led. Also, underplay a numerical trump, risking the chance of your partner winning it. We have acquired antipathy to a single lay card and love to dispose of its bachelor-like wretchedness by embracing the first opportunity.
So often as the lead changes the relative positions of the players -as the leader, second, third and fourth player -also vary, of course.
Second player following suit to lay cards, as a general rule, should always head, that is win the trick, if he can. The same, with few exceptions, when playing trumps.
With one trump only, if the Right-Bower himself single, and your partner adopts or makes the trump, ruff with it the first chance.
When you can neither follow suit nor trump, throw away the weakest card you have, naturally.
In the situation of third player your "officious duties" become more onerous. When playing to win a Euchre, if you hold a small and a medium card, at trumps, and have the opportunity to ruff, stick in the medium trump, if third player, which may force the dealer to play his best trump. Never send a boy, you know, on a man's errand. And this, by-the-by, reminds us of a pretty problem in play. Suppose yourself sitting on the right hand of the dealer who has turned the Knave of spades, and adopted the trump. Two rounds have been played -the first trick having been won by your opponents, and the second by your partner. Your partner leads in a lay suit and is followed by the second player, and you hold the Left-Bower, Ace, and Queen of trumps, you play either the Left-Bower, or Ace, and the dealer holds the Right-Bower, King, and ten of trumps. If the dealer takes the trick with the Right-Bower, which he would naturally be inclined to do, he is Euchred, because you then have the tenace.
But, on the contrary, if he should play the ten of trumps and let you win the trick, he gains the odd-trick, as by this underplay he secures the tenace to himself. If you had played the Queen -which would have been a horrid play -you would, of course, have lost the odd-trick. This simple problem is deemed worthy of especial commendation, as illustrative of the peculiar advantage of the tenace.
You should be very strong in trumps to order up, because your partner, passing, shows that he is weak, or prefers to make the next in suit. As a general rule let the responsibility of ordering up rest with your partner, when he is eldest-hand.
When your partner has adopted or made the trump, be careful not to win the lead from him, unless you are strong enough to play for a march, or to win the odd trick.
Always divest your hand of losing cards, when possible, to your partner's winning ones.
If your partner in the third or fourth round leads a lay King (you having none of its suit) which is not captured by your right-hand adversary, with trumps, throw it away on your partner's lead, for his King having passed safely through one hand is much more likely to win than yours would be, having to pass through both hands. Trust it through one hand rather than two is the rule. Play in like manner in like cases, you understand.
Special thanks to Todd Martin
Opportunities to finesse occur but rarely, and when they are offered should be exercised with considerable caution. It is much better for the third player to win the trick than risk its loss by any delicate stratagem of play.
The vocation of the dealer is replete with interest. He should commence by distributing the cards with exactness, not allowing any card to be exposed, except the one turned for the trump, or his antagonists may declare the deal null, and he will have to perform it afresh. He should always discard a single card, though above medium value, and retain two of suit, if one of them is not higher than a nine. When he determines to Play Alone with three trumps, he should always discard even so high a card as a King of a lay suit when the only card of the suit, and retain the seven, or any other card, of a suit of which he holds the Ace, for the chances are much better that the Ace will exhaust the suit and let the seven win, than that the King would win the first time round.
If his partner, assisting, has played one trump, the dealer winning a trick should never lead him a trump, unless he is sure of winning the march, or the odd trick, with his own hand; for the probability is that his partner has assisted with two trumps only, and by leading a trump to him he may draw the last he holds, and in that way entirely destroy his game. This is a fatal mistake but often made by inexperienced players, and is conspicuously improper, as you see. But if your partner assists, and your side have captured the first two or three rounds, leaving you with commanding trumps and sure lay cards, win the lead from him then and secure the march, for he might be left to lead a losing card not of your sure suit.
Always when assisted, Mr. Dealer, and you hold the card next higher or lower to the trump card, play it instead of the trump card for your partner's benefit. -Thus, if you turn up a King, and also have the Ace in hand, and your partner assists, when a trump is led, or you can ruff a suit, and should play the Ace, which shows your partner that you have the King left. continue
Note: Natty Bumppo, author of "The Columbus Book of Euchre" - (1982), believes that A. Professor was actually  named Charles Henry Wharton Meehan.