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The Official Rules and Laws of Euchre
Standard euchre game rules:
The Deck: 24 cards    
The ace, king, queen, jack, ten and nine of; clubs, diamonds, hearts and spades.  
Players:   4 
Two teams consisting of two players each are seated across from each other.
Object:
The Deal:
Five cards are dealt to each player. The four undealt cards (known as the kitty) are placed facedown on the table. The top card of the kitty (21st card of the deck), is turned faceup. It is commonly called the upcard.
Making Trump:
  Beginning with the player to the dealer's left and proceeding clockwise, each player in turn has an opportunity to accept the suit of the upcard as trump, or to decline by saying "Pass." If the upcard is accepted as trump by any player, that player tells the dealer to "pick it up." If it is the dealer, he needn't say anything. Picking up the card is self-explanatory.
  The dealer then takes the upcard into his own hand and discards one face-down.
  If all four players decline, the upcard is turned down and each player in turn--again beginning to the dealer's left--may name any suit except the former upcard's suit as trump, or may pass. If everyone passes, the deal is thrown in and the next dealer deals.
  The player who chooses the trump suit, either by accepting the upcard's suit as trump, or by naming a different suit, is called the maker. Before the play of the hand begins, the maker may announce; "Alone", in which case the maker's partner places his hand facedown and does not participate in the play.
The Play:
  The player to the left of the dealer leads any card by placing it faceup on the table. Each player in turn, moving clockwise around the table, must play a card of the same suit that was led if able. If unable to follow suit, a player may play any card. When all four players have played a card, the "trick" is complete. The trick is won by the player who played the highest trump, or if no trumps were thrown, by the one who played the highest card of the suit originally led.
The Rank:
In the trump suit, the highest card is the jack, called the "Right Bower." The second highest card is the jack from the suit that is the same color (black or red) as the trump suit, called the "Left Bower". The third highest is the ace, followed by the king on down to the nine of trump; Right Bower-Left Bower-A-K-Q-10-9.
The non-trump suits are ranked ace high down to the nine; A-K-Q-J-10-9. One suit will be without a jack, as this card will become the Left Bower.
Example: Hearts are trump
1. Right Bower
2. Left Bower
3. Ace
4. King
5. Queen
6. Ten
7. Nine
Scoring:
The maker's partnership scores 1 point for taking three or four tricks, or 2 points if they manage to take all five tricks (known as a march). If they take fewer than three tricks however, they are euchred and score nothing -- instead, the defending side scores 2 points.
A maker who opts to play alone (without his partner) can score 4 points for taking all five tricks. The lone player can only score 1 point for taking three or four tricks. Taking two or less of the tricks alone will score 2 points for the adversaries.
Revoke :
A player revokes (or "reneges") when they fail to play a card of the suit led, if in fact they have one.
2 points are automatically awarded to the opponents of the guilty party, the hand is ended immediately upon discovery and the deal is forfeited.  If the guilty team is defending against a lone-attempt during the infraction, 4 points are awarded to the team that was attempting the loner.
According to
The makers (the partnership of the player who named or ordered trump) must try to win at least three of the five tricks. Taking three tricks or more will score points, while failing to adds points to the opponent's score instead.
The Official Laws of Euchre
II. The cards must be shuffled by the dealer and may be cut by his right-hand opponent. The dealer should never hold the deck in his hand when presenting it for the cut, but instead should place it on the table near his right-hand adversary. The latter also has the privilege of shuffling them, and if he does, the dealer, who is always entitled to the last shuffle, may shuffle them again if he chooses. After the cards have been cut for the deal however, no one except the dealer, can touch the deck prior to dealing.
III. In dealing, five cards are distributed to each player, either by three and two, or by two and three, in two rounds; but the dealer must continue to follow whichever mode he at first adopts, and should he depart from it, either of the adverse parties may, before looking at his cards, require a fresh deal.
IV. If a card is exposed, or is turned in dealing, unless it is the twenty-first card (which is normally turned up anyway), the same dealer re-shuffles. Should the dealer show more than one card while turning up, the deal is likewise void, but again, the same dealer re-shuffles.
V. Should either of the dealer's opponents, during the deal, expose a card, the dealer may have a fresh deal, or not, at his option, but he must decide before looking at his own cards. If the dealer's partner exposes a card, either of the adversaries, before the upcard is turned, may request a new deal.
VI. No player is permitted to take up, or to look at his cards during the deal, and should a misdeal occur, the dealer does not lose his privilege and may deal again. It must be considered a misdeal however, if the dealer's  partner commits the fault.
  Aside from the rules above, any variation should be agreed upon by all parties prior to a game in order for the variation to be in effect.
I. To determine who the players will be in a euchre game, the cards need to be shuffled by one (potential) player, then passed to the right for a cut. The person who cuts should then deal one card face up to each person who wants to play, starting to their left and continuing clockwise. The player who receives the first jack will become the first dealer when the game begins. The cards should be dealt in this manner, skipping players who already have jacks, until all four bowers are dealt. The players with the same-colored jacks will be partners. Players that don't receive a jack must sit out.
VII. When too few or too many cards are dealt, if the mistake can be rectified, and the proper order of the distribution of the cards ascertained before the 21st card is turned up, the deal is valid; but if the error is not discovered until after it is turned, the deal is forfeited, and passes to the next player.
VIII. If the cards are dealt by a player who is not entitled to the deal, and the error is discovered before the turned-card is up, the cards must be restored to the player entitled to the deal. If the dealer has turned up a proposed trump card however, the deal stands. The current dealer's left-hand opponent will deal the next hand.
IX. If, in any deal, the pack is ascertained to be imperfect, by containing too many, or too few cards of the proper value in any suit, that particular deal is void, but all the games or points made in the preceding deals with the same deck are valid; and the deal in which the error is discovered is not forfeited.
X. The dealer may leave the trump card in view on top of the kitty until it is his turn to play. At this time, he must remove it to his hand. After he has taken up the trump card, no player has a right to demand what particular card was turned up, although he may ask what suit is trump.
XI. Whenever a misdeal occurs, the deal is forfeited and the opponent to the left gets to deal.
XII. Each person, in playing, should place his card on the table immediately before him, but if this practice should not be pursued, no player has a right to ask who played a particular card, although he may require the other players to draw their cards before them.
XIII. If the eldest-hand leads before the dealer has discarded, he cannot withdraw his card and change his lead, nor can the dealer be deprived of his right to play alone. The discard is not completed until the dealer places his card under the kitty, or on the table, and has quitted it; and when the dealer has once quitted the discarded card, he cannot change it.
XIV. If a player leads, or plays out of turn, he may be compelled to withdraw his card, subject to the penalty of the call; if it causes an error in the play of any other party, that player may withdraw his card without penalty; but, in the case of an improper lead, if four cards have been played before the error is discovered, the lead is good and the player winning the trick is entitled to the next lead.
XV. Any card which is separated from those in hand and has touched the table, is deemed to have been played- even if the face be downward - though if a card is played to a lead of a suit different from the one led, it may be taken up, subject to the call, and another of the proper suit played. But if the player should have none of the suit led, and plays a card which he did not intend, he is not permitted to take it up again after he has once quitted it.
XVI. If a player plays two or more cards to a trick instead of one, the adverse parties have the right to compel him to play either one of the cards they please, without regard to the order in which they were played, and the other card, or cards, shown may be called in the subsequent tricks, like other exposed cards.
XVII. No player is allowed to look at any of the tricks during the play of a hand, after they have been turned, except the last trick played only.
XVIII. If any player plays with six or more cards, or, if the dealer plays and omits to discard and fails to announce the fact before three tricks have been turned, such player or dealer cannot count the point, or points, made on their side in the hand, and they lose the deal. But if the adverse party win under such circumstances, they are entitled to count all they make.
XIX. If a player, designedly, or for any reason, places his cards on the table, faces turned up, he is not permitted to take them up again, and his adversaries may call each card like other exposed cards. Thus, if a player, sure of winning, exhibits his cards, his opponents can continue the play, and have the right to call each card so exposed. The penalty is the same if a player believing he has lost shows his cards in a similar way.
XX. Whenever a player, who is entitled to the privilege of making the trump, once names a suit, he cannot be permitted to change it, and should he, by mistake, name the suit turned down, it is equivalent to passing, and the right to make the trump then belongs to his left-hand opponent.
XXI. A player intending to play alone must announce his determination to play without his partner in such an audible and distinct expression that no doubt must exist of his intention, for if his manner of announcing it is ambiguous, and a legal lead is made, by himself or an adversary, he loses the privilege of playing alone and must be compelled to play with his partner.
XXII. The revoke is not completed until the trick in which it has been made is turned and quitted, and the player committing the revoke, or his partner, has again played.
XXIII. If a player revoking perceives his error previous to the turning or quitting of the trick in which it has been made, he can withdraw his card from the trick and follow the suit led, but his left-hand antagonist may compel him to play the highest or the lowest card he holds of that suit; or, if it seems more advantageous to his side, he may call the card so exposed and taken back whenever it is the offending player's turn to play, or lead, in a subsequent trick.
With the utmost respect for the work of:
A. Professor   -1862
abridged and adapted in 2006   more
XXIV. If the partner of a player, who has made a revoke, but has discovered it in time to correct it, has played to the trick, he is not permitted to change the card he has played, but the adversary who has played after the revoke occurred may withdraw his card from the trick without penalty, and play another, if he thinks it may give him and advantage.
XXV. Should either of the adversaries mix the cards together when a revoke is alleged against them, they incur the penalty of the revoke, and the players claiming it are entitled to score the two points.
XXVI. When the cards have been cut for a new deal, no party is entitled to claim the penalty of a revoke; and, in case of a reciprocal revoke in one hand, one error offsets the other, and a fresh deal must be had.
XXVII. If a player shows or exposes one or more of his cards intentionally or by accident, the card or cards so shown may be called by an opponent, either as a lead, when the offending player's turn to lead, or to the exposed card's suit when led. A card is shown if it is purposely, or accidentally exposed, and either of the opposite players can distinguish its character, and name it.  In addition, a card may be called if the holder names or indicates that it is in his hand.
XXVIII. A player called upon for an exposed card must play the card or submit to the penalty of a revoke.
XXIX. The right to call one or more cards, improperly played or exposed, by an opponent, belongs only to the left-hand adversary of the offending player. In no case can such a card be called if it causes a revoke; nor, can the player entitled to call, require his opponent to throw away a commanding card to a lead of different suit, when holding no card of the suit led, whether he can trump it or not. If two or more players, in any one deal, expose a card, the law is the same.
XXX.  Neither adversary is permitted to call the attention of his partner to the state of the game at the bridge without forfeiting their right to order up, and the dealer, or his partner, may then play alone, or not, at the option of either.
XXXI. If the counter marks more points than he is entitled to score to the game, either adversary - or bystander even - may call attention to the error, and the opponents are entitled to count to their score, the point, or points, which their adversaries erroneously added to theirs. But the error cannot be rectified after the trump card has been turned in the deal next ensuing that in which the error occurred. So if he fails to count, or counts fewer points than he is entitled to, he loses the right to score such point, or points, when the next deal is completed.
XXXII.  Should a player from loss of temper - or upon supposition that he has lost or won the proper number of tricks - or from any other cause - throw down his cards upon the table, with their faces turned up, he cannot take them in hand again, and his left-hand adversary may call each card so exposed as he deems most advantageous to his side. Who leaves the game loses it, is a maxim of this as of all other games.
XXXIII.  Every species of unfairness is strictly prohibited; and if a player, at any time between the turning up of the trump card and the playing of the last card of the deal, indicates to his partner the strength of his own hand, either by words or gestures; or advises him how to lead or play; or invites him to make a trump, by such expressions as "follow the rule," "make it something," or any similar phrase; or, asks any questions about the game except such as are specifically allowed by the Laws of Euchre, the adversaries shall immediately add one point to their game.
XXXIV.  In every case of a penalty which entitles one party to add a point, or more, to the score of their game - for the revoke, or any other wrong practice in play, - the offending party cannot count a point, or more, which they may have won in that deal - or round - in which the penalty was incurred; and the regular routine of the deal continue.
XXXV. Every penalty incurred by the misconduct of a player must be shared and submitted to by his partner - for partners are mutually responsible for each other's faults.
XXXVI. If a player who has incurred a penalty imposed by a provision of any of the preceding Laws, refuses submission to such penalty, his opponents may immediately throw down their cards, and that game, at any state of the score, is declared to belong to them.
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Variations :
Variations are rules that are employed in addition to the standard euchre game rules. In many instances, the variation will over-ride parts of the standard rules.
A checklist of variations are available here.
Keeping score can be done in a variety of ways (scorecards, pegboards, chalkboards etc.), but most importantly, the method adopted must be agreed to and understood by all parties prior to engaging in play.
The side marking a score should announce their total in an audible voice when doing so. The adversaries have until the time the next upcard is turned to challenge the scoring, otherwise the score stands as marked.
The player sitting closest to scorekeeping device is responsible for marking it correctly. He may be reminded by his partner or any outside party however.
To be the first team to score 10 points.
According to
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