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Definition 1

general: An unexpected bet (bet out of nowhere) that isn’t transparent to the opponents, as it seems to be out of sync with the previous betting sequence.

Definition 2:

A risky and egocentric bet, ignoring the danger coming from both the board and opponents who show strength. Often indicates weak players that play their cards in a tenacious way (like a donkey) and do not seem to care for their opponents’ actions. Such players might e.g. bet their top pair out of position even if the board offers straight- and flush-possibilities, or if the action indicates that an opponent already has “2 pair or better”.

Definition 3:

A donkbet by a strong player might be attributed to a stop-and-go-strategy.

Donkbetting the turn:

The most common donkbet. Usually means betting the turn in early position against the flop-raiser.

Heads-up against the flop-raiser

Heads-up against the flop-raiser after you played check-call or bet-call at the flop:
You do this with really strong hands (like a set) against an aggressive opponent, hoping to catch a raise you can reraise him. That way you can win more chips than with the more common idea “check-raise the turn”.

The psychological advantage: You hope that your lead bet at the turn is being sensed as a bluff and countered by another semi-bluff.
The financial advantage: You hope that your opponent holds an expensive second best hand (like AK, flopping an A, while you hold a set) and aggressively raises for value.
The positional advantage: Your opponent doesn’t get the chance to get a free-card.
The gravity advantage: You don’t let your opponents leave the hand that easily. A standard “check-raise turn” is a much better exit for many opponents.

Garandou provided us with the following example:

Party Poker 5.00/10.00 Hold'em [color:#0000FF](4 handed) link

Preflop: Hero is SB with 6 , 6 .
UTG calls, 1 folds, Hero raises, BB 3-bets, 1 folds, Hero calls.

Flop: (7.00 SB) 6 , 5 , J (2 players)
Hero checks, BB bets, Hero calls.

Turn: (4.50 BB) 5 (2 players)
Hero bets, BB raises, Hero 3-bets, BB calls.

River: (10.50 BB) K (2 players)
Hero bets, BB calls.

Final Pot: 12.50 BB