Air Hockey
Play air hockey, plus the exact bank-shot mirror rule and the measured reason banking costs you precision and time without beating anyone.
Move your mallet with the mouse or a finger; you are the lower half. Everything runs in your browser; nothing is uploaded.
The bank shot is a mirror, exactly
To bounce a puck off a side wall into a target, reflect the target across that wall and aim straight at the mirror image. Reflect again for a second bounce, and so on. This is not a rule of thumb — unfolding the table and drawing a straight line traces the same path as folding the puck off the walls.
Checked against a stepped simulation across the full range of aim points: the worst disagreement anywhere is 2.8e-9 of a table unit, and the bounce counts match every time.
| Bounces | Aim at the unfolded point | Aim window | Path | Flight time | Arrival angle |
|---|---|---|---|---|---|
| 0 | x = 150 | 7.63° | 600 | 1.00× | 0.0° |
| 1 | x = 450 | 6.82° | 671 | 1.12× | 26.6° |
| 2 | x = 750 | 5.40° | 849 | 1.41× | 45.0° |
| 3 | x = 1050 | 4.24° | 1082 | 1.80× | 56.3° |
| 4 | x = 1350 | 3.42° | 1342 | 2.24× | 63.4° |
Shooting from the middle of your own goal line at the far goal, on a 300 × 600 table with a 80-wide mouth.
And it costs you on every axis that can be measured
The target never gets smaller — the goal mouth is the same size wherever its image lands — but it gets further away. So the angle you have to hit shrinks from 7.63° for a straight shot to 3.42° at four bounces, less than half as forgiving.
And the puck travels further every time — 2.24× the distance at four bounces, which is 2.24× as long for the defender to reach the spot. Harder to aim and slower to arrive.
Which leaves the usual justification: bank it to get around the defender. The geometry refuses that flatly. A bank shot arrives at the same point on the goal line as a direct shot at the same target — that is what it means to have aimed at the target's mirror image. Anyone standing on that point stops all of them equally, whatever the bounce count.
What banking actually buys is the angle the puck arrives at — 0° straight on, up to 63° after four bounces. And it buys deception: a banked puck sets off in a direction that does not point at the goal, so a defender reading your aim can be sent the wrong way. That is real, and it is a fact about the person rather than the table, so nothing here measures it. What the numbers do settle is that a defender already standing in the right place will not be beaten by geometry.
How to use
- Move your mallet with the mouse or a finger; you defend the lower goal.
- Strike the puck by moving into it — the mallet’s own motion adds to the shot.
- To bank off a side wall, aim at the mirror image of your target across that wall.
- Reflect the target twice for a two-bounce shot, and so on.
- Compare the aim windows in the table before trusting a bank shot.
Frequently asked questions
How do you aim a bank shot in air hockey?
Reflect the target across the wall you want to bounce off and aim straight at the mirror image. For two bounces, reflect twice. This is exact rather than approximate: unfolding the table and drawing a straight line traces the same path as folding the puck off the walls, and checked against a stepped simulation the two agree to about a billionth of a table width.
Does a bank shot get around the defender?
No, and this is the part that surprises people. A bank shot arrives at exactly the same point on the goal line as a direct shot at the same target — that is what aiming at the mirror image means. Someone standing on that point blocks every version equally, whatever the bounce count.
So what does banking actually cost?
Precision and time. The goal mouth never gets smaller, but its mirror image sits further away, so the angle you must hit shrinks from 7.63 degrees straight on to 3.42 degrees after four bounces. The puck also travels 2.24 times as far, giving the defender that much longer to arrive.
Then why bank at all?
Two reasons. The arrival angle changes — from straight on to about 63 degrees after four bounces — which matters if the defender is covering a line rather than a point. And deception: a banked puck sets off in a direction that does not point at the goal, so an opponent reading your aim can be sent the wrong way. That second one is a fact about the person, not the table, so no measurement here covers it.
How many bounces are worth using?
On the numbers, as few as will do the job. Every extra bounce narrows the aiming window and lengthens the flight, and neither ever reverses. A bank shot is worth taking when the deception is worth more than the precision you are giving up, which is a judgement rather than a calculation.
Does this send anything anywhere?
No. The game and the geometry both run entirely in your browser and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.