Why play a Gambit?

Very rarely have I encountered a player that fell for (decided) taking a piece like that.  I thought we shouldn't base our strategy on hope.

Usually its best to accept a gambit which means that not accepting certain gambits can be advantagous for the one playing the gambit. You just have to understand what to do in both cases.

1. Learn to attack 2. The concept of dynamics in position 3. Learn to use your development advantage 4. The concept of the price of each tempo in an open position 5. Using pawn dominance in the center 6. The concept of initiative 7. Greater likelihood of tactical ideas 8. Concept of using compensation.

Most gambits are unsound.
The refutation is to accept the gambit, defend, and simplify to a won endgame.
The compensation evaporates but the material deficit remains.

So gambits are designed to benefit the side playing them if the other player doesn't take material. QGD you gain central control and pressure on d5. KGD the same. Evans gambit, you gain space on queenside or win a bishop if black isnt thinking (won a game this week in bullet because of that), danish gambit you get a full centre. Centre counter gambit (Scandi) black pushes on and cramps development of white. There is always some trade off, but you need to know what you are doing.

Gambits can create psychological pressure on the opponent, especially if they are not well-prepared or uncomfortable facing unconventional openings.

Also, they are forcing. Even losing gambits require accurate play to punish; by forcing your opponents to find the series of good moves in your gambit opening that don't hand you a piece or a decisive position, you burn their clock and give yourself a time advantage.