Elements of Euchre
A breakdown of the most basic strategies.
  Before one can really accomplish any sort of mastery of the 24-card deck, they should have a good visual picture of the deck as a whole. Provided here is a picture of the deck that a euchre player should keep in mind at all times.
  Although euchre is played with a 25-card deck that includes a Joker (or "Benny") in the British Isles, and many popular rule books include the 7's and 8's for a grand total of 32 cards, most euchre players in North America, Australia and New Zealand use a 24-card deck that includes only the 9's through Aces.

- Singletons, Doubletons etc.
- Not having a card of a particular suit is called a "void".
- Having a "singleton" simply means that you have only one card of a particular suit. "Doubleton" of course means two cards (from the same suit) and "tripleton" is three.
- Leading a singleton Ace is more likely to win a trick than a doubleton or tripleton Ace. This is simply because the more cards you are dealt of a suit, the more likely that someone else at the table is void in that suit. The opponents have more of an opportunity to trump your Ace.

The Guarded Left
Left Bower + X
In the example to the left, Clubs are trump. The Jack is the Left Bower and is considered to be guarded by the nine in this case, although the Left Bower can be with any trump lower than itself to be considered guarded.
When a player holds this on defense, that is, when the opponents are the makers, these two cards together should constitute a certain trick. This is assuming the holder is able to play the smaller (x) card on the correct trick, which is the same trick that the Right Bower is played (assuming that it is not burried in the kity).
When the Right Bower is led, the lower card is played and the Left Bower becomes promoted to the highest trump in the deck. Playing either card before the Right Bower comes out, only to take a lesser trick is known as "unguarding the Left" and is largely a mistake.
The Guarded Ace
Ace + X + X
This example shows a guarded Ace; which consists of the Ace of trump and two lower trump cards. Even if the opponents lead the Right and Left bower (back to back ), the player with this  holding can lose the queen and nine and still hold a sure trick to stop a march.
Once again, it is a mistake to unguard this holding by trumping an off-suit lead with an opponent yet to play a card.
Sometimes circumstances beyond your control will warrant it though. An example of that would be if your right hand opponent called Clubs and led the ten of Clubs to you. If you discard low, your left hand opponent could drop the king of Clubs on it. This would leave two bowers out there that could take both of your remaining trump. If you choose to play the Ace against the maker's ten, the left hand opponent may have a bower, leaving open the scenario that your side won't stop the march.
It's a crap shoot.
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This page was created with the intention of giving the reader a clear image of "the big picture" of euchre strategy.
  The most basic strategies are broken down here into their simplest form.
-Harvey "the Rabbit" Lapp
1. Knowing the 24-card euchre deck.
Picture of the 24-card deck
Notice that there are four suits and that each suit contains six cards. That is, until a suit is made trump. Euchre is a rather unique card game in that when a suit is made trump, the suit count actually changes.
Take a look at the same deck of cards when Clubs are trump, just for an example;
Clubs are trump
Notice that there are now seven cards in the trump suit, six cards each in the two other color (or "green" suits), and only five cards in the same color (or "next" suit).
Although it might not seem like that big of a deal at first, anybody with minimal knowledge of probability will realize immediately that it will be more likely for all of the players to have a trump Club in their hand and less likely to have a Spade, after the cards are randomly shuffled and dealt. This is a good notion to keep in mind while playing euchre because it gives you a basis of expectation whenever you lead a card.
In the case of Clubs being trump, if a Spade is led first, there is a likelier chance of a player not having one than there is if a trump is led.
2. Distribution
The deck is shuffled, hopefully leaving them in random order, then five cards each are dealt to all four players at the table. That accounts for cards #1-20 of the deck.
The dealer then turns over card # 21, for all to see. All four players now have knowledge of the five cards in their hand plus the upcard for a total of 21 cards.
Cards #22, 23 and 24 however is where the mystery lies. This is part of the fun of euchre, not knowing what those three cards are in the "kitty". You just never know for sure if the cards that can hurt you are in play or not. It also makes it especially tricky when devising a bidding strategy. A hand that scores two points one time might only score one the next, or even get euchred against a very bad distribution.
A much more in-depth mathematical page about distribution
- Other notable Holdings:
The Tenace

The tenace is not actually related to a ten and Ace combination but in fact any sequence of valuble cards in the same suit which are not adjacent in rank. This would include a suited Ace-Queen, or Left Bower- King combination (and others). A tenace isn't neccesarily trump, but euchre is such a short-handed game, a non-trump tenace any less than Ace-Queen is hardly anything to worry about.
For the example to the left, I've chosen the grandest of tenace holdings of them all in euchre, the Right Bower - Ace combination.
With these two cards in hand, if one plays the Jack before the Left Bower surfaces, the Left may remain in play for a subsequent trick, making the Ace a loser. The key to successfully taking two tricks with these cards is to take down the Left Bower with the Jack.
3. Bidding
The subject of bidding is a particularly difficult subject when it comes to euchre. There are large volumes of books written about the subject of bidding at Bridge, but in Euchre, it becomes much more of a guessing game. Although the deck is much smaller, an eighth of it is not even in play during a hand. Although a point count system like one Goren devised for Bridge will not always hold up in Euchre, Perry Romanowski has devised a system that will give a player a good method of evaluating one's hand when deciding whether or not to bid.
Romanowski's Euchre Point Count
Euchre is a bit of a crapshoot mathematically, and hands that will sometimes win, will also sometimes lose. It is professed by many euchre experts that not bidding in hopes of euchreing the opponents will become a losing proposition over the long haul. The best evaluation of hand strength indeed comes from playing many hands.
The following concepts are compiled from various works and experiences and should help to provide a theoretical basis for bidding in euchre, if the reader does so choose.

- Count on your partner for a trick.
-This concept is simply an old adage that really does have some substance to it. Sure, your partner won't always have a trick, but by assuming that she does, you'll be calling more trump than normal, thus not playing too conservative to give yourself a chance to get lucky. Just like the lottery advertises; You gotta' be in it to win it!

- Consider bidding two-suiters.
- When you have two voids, there are three suit leads that you are capable of playing trump on. That increases a hand's power significantly. Even though you are holding the 9-10-Q of one suit and 9-10 another, you may consider the bid, depending on a variety of other factors.

- Bid "Next".
-  If you are sitting in the first seat left of the dealer, you can consider bidding an ordinarily weak looking hand in the suit that is the same color as the former upcard. This is commonly known as bidding "next".
You are basing this call on the fact that the opponents have both passed on a suit possibly because they do not have any Jacks of its color. You are hoping of course that any cards that are not in your hand that could help you are in your partner's hand or burried in the kitty.
Many of the euchre experts aggree that holding a "green" off-suit Ace is a must when bidding a very weak "next" bid.

- Bid "Reverse Next".
-  If you are the dealer's partner and all of the players have passed, and the opponent in first seat has not bid "next", you should consider bidding "reverse next". Reverse next is the suit that is "green", or one of the suits that is not the same color as the former upcard.
You are basing this call on the fact that your partner did not pick-up the upcard and the player to your right didn't have a strong enough hand to order. Your partner is more likely to have some help in a suit of another color, since he passed on the advantageous edge of being able to discard and play last.
Just how weak can you go? Experimentation has shown that simply having a "green" King and nine with a "next" singleton Ace is about a 50/50 proposition. This hand is known as the K-9 Kicker and is explained in full at this link:

The K-9 Kicker