Simply put, cards can be dealt out in any manner approved by the table, so long as all cards are dealt out with none leftover. One side note: A common way to deal double deck Euchre is 3 or 4 cards each time around.
The big difference in Bid Euchre, as the name implies, lies in the bidding. Instead of a "First come, First served" type of bidding, each player gets a change to bid on the number of tricks and the trump suit involved with which they can win the points for the hand. If a double deck option is utilized, the bidding is based on twice the number of tricks of a single deck. Since the bid revolves around the freedom to make any suit trump, no Kitty or Turned-Up Card is necessary. The second round of bidding is also eliminated as each player is guaranteed a chance to bid any suit in the first, and only, round. The number of cards dealt out is based on house rules. From a regular Euchre deck of 24 cards, each player would receive 6 cards, hence bidding is based on 6 total tricks. Using a double deck, there would be 12 tricks. Some tables leave the nines out in Bid Euchre so that the total number of tricks would be 5 or 10, depending on the number of decks used. The bidding order goes around as usual. The first bidder calls the number of tricks they think they can take as well as the suit they wish to call trump. No-Trump can be called if the table allows this as a play option. Also, if a player is dealt a lousy hand, they can pass. All subsequent bidders can bid or pass in order. The 2 key rules in bidding after other players are that: 1) all suits are considered equal, and 2) the bidder must "Over-Bid", else pass. This means that "6 hearts" can be followed by 7 (or higher) of any suit, but not 6 (or lower) of any suit. If a bidder is unable to "Over-Bid", they must pass. Going alone is another bid that can be used. Railroading can be utilized for 1 or more cards depending on the house rules. If all players pass (which is uncommon but can happen), the cards are thrown in and the next dealer in the rotation deals a new hand. After a successful round of bidding is over, the highest bidder (traditionally) leads off the first trick.
For the duration of the rest of the hand, the gameplay is the same as regular Euchre. As a double deck is often utilized, keep in mind if the same card is played twice in a trick, the first player to throw that card ranks higher.
Scoring is the second major difference between regular and Bid Euchre. Traditional scoring is performed as follows. If the bidding team collects at least the number of tricks they called for, each team gets 1 point for each trick they took. If the bidding team is "euchred", they lose the number of points equal to the number of tricks they bid, while the defending team still wins a point for each trick taken. The number of points at which the game is won is determined by the house rules (a common goal is 32 points, or 96 if doing an all-niter).
A team must win either by taking the required number of cards on a bid or by euchring the opposition. They cannot win by reaching the goal with the trick points earned defending against an opponent's successful bid.
As mentioned in the previous page, I will be defining a game option or variation as an individual trait of the gameplay which is not consistent among all games or Euchre circles. The term "style" will be used to describe a type of gameplay which utilizes any number of set variations consistently. Keep in mind that "styles" are usually named geographically and are not meant to be strict and universal constraints placed upon the regions mentioned, hence names will be in quotations.
Threshold Scoring - In this, a team can win the game by scoring the required number of points in any fashion.
HiLo No-Trump Bidding - With this option, as the name implies, bidders who call No Trump have the choice of making a "No-Trump Hi" bid which means cards are ranked with Aces high and other cards in order progressively lower (this is standard for No-Trump) or making a "No-Trump Lo" bid which means the opposite, i.e. cards are ranked with Aces low and other cards in order progressively higher (in essence, if a player has a handful of pitifully low cards, they can still turn their hand into points with a "No-Trump Lo" bid).
Triple Threat Loner - Bidding is standard as described above, but with a twist for going alone. First, a player must take all the tricks in the hand if they go alone. As such, this is the "highest" bid just above bidding to take all the tricks with your partner. Second, railroading is allowed in 1 of 3 ways: the loner may ask for 0, 1 or 2 cards from their partner to exchange for their worst. The loner, if successful, earns 4 points extra (plus their trick points) if 2 cards were swapped, 10 points extra if 1 card was swapped, and 16 points extra if the loner marches with what they were dealt (called "shooting the moon"). If the loner is unsuccessful, they lose the number of points equal to that which they stood to gain had they been successful. This type of game is usually played to 52 points, but house rules may vary. Variances can also be implemented in extra points awarded and/or number of cards allowed to be swapped.
Auction Bidding - Bidding with this variation in place continues past the first round in an auction type format. Players can continue to bid higher and higher until one player is not outbid by any other player. As in triple threat, the highest bid is going alone, i.e. taking all tricks in the hand solo (why did a vision of a young Harrison Ford just pop into my head?).
Nelo - This is a bid used in the game Five-Hundred (similar in style to Bid Euchre as well as a Nil bid in Spades) in which a player goes alone in an attempt to not take any tricks. The objective of the opposition, in turn, is to make the bidder take at least one trick. Scoring is various per house rules but usually consists of the bidder earning a fixed number of points if successful and losing a fixed number of points as well as points for each trick taken if not successful. Railroading may or may not be utilized.
Dealer's Privilege - The dealer, with this, may make trump by matching the highest bid (in number, any suit).
Variable Player Number - Just as mentioned in the previous page, Bid Euchre is by design a 4-player game. It can, however, be played with more than 4 players. The styles section lists some popular variations based on this principle.
Point 6 Screw the Dealer - This is very much like "Screw the Dealer" in the Variations page. The dealer, after all players have passed, must bid to take at least 60 percent (0.6) of the cards. With hands of 5 cards, the dealer would have to bid 3 of something. If hands are 8 cards, the dealer must bid 5 of something (which is actually 62.5% but such is life).
Bidder's Pet - In variations in which a Kitty is involved, the highest bidder is permitted to exchange their worst cards for the cards in the Kitty. This can either be done by laying the appropriate number of cards down, then picking up the Kitty (called "Discard/Pick-Up", preventing the highest bidder from retaining only the useful cards of the Kitty), or by picking the Kitty up first then discarding (called "Pick-Up/Discard", allowing the highest bidder to pick and choose which cards they want to play with) depending on the house rules.
Cutthroat - This is the same concept as the Cutthroat option shown on the previous page. The only real difference is the way the game is scored. Below are several Cutthroat styles.
"Hoosier Bid Euchre" - A 40-double deck is used. Players are in a partnership and each receive 10 cards (no Kitty). A bid of No-Trump (Hi only) is permitted. "Shooting the Moon" is worth a 6 point bonus if done with a partner, and 12 points bonus if gone alone (positive or negative depending on success). Additional players can be added by increasing the deck by 10 cards per extra player. The game is won at 32 points.
"Hoosier 3-Player Bid" - Cutthroat rules apply. A 32-double deck is used. Players each receive 10 cards with a 2-card Kitty used as "Bidder's Pet (pick-up/discard)". A bid of No-Trump (Hi only) is permitted. "Shooting the Moon" is worth 12 points bonus (positive or negative depending on success). Additional players can be added by increasing the deck by 10 cards per extra player. The game is won at 32 points.
"Purdue Cutthroat" - Cutthroat rules apply. A 24-single deck is used. Players each receive 7 cards with a 3-card Kitty used as "Bidder's Pet (pick-up/discard)". A bid of No-Trump (Hi only) is permitted. "Shooting the Moon" is worth 16 points bonus (positive or negative depending on success). The game is won at 32 points.
"Shawn's Bid Euchre" - A 32-double deck is used. Players are in a partnership and each receive 8 cards (no Kitty). Minimum bid is 3 tricks with a trump suit or 5 tricks if No-Trump. Lone bids are permitted of 7 or 8 tricks, with 7 alone ranking between 7 and 8 with a partner and 8 alone being the highest bid. 7 alone is worth a 7 point bonus (positive or negative) with 1 additional point if all 8 tricks are taken. 8 alone (shooting the moon) is worth an 8 point bonus (positive or negative). The game is won at 32 points.
"Racehorse" - A 24-single deck is used. 6 or 8 players may play with a 48-double deck. Players are in a partnership and each receive 6 cards, or 8 cards in playing with 6 players (no Kitty). Bidders only bid the number of tricks, then the trump suit if they are the highest bidder. Minimum bid is 3 tricks with Dealer's Privilege. Lone defenders are permitted. Scoring is per Regular (non-Bid) Euchre rules. The game may be won at 10 points, 11 points (a five and a six used to keep score) or at 15 points (a seven and an eight used to keep score).