Billiards online: angles and bank shots
Billiards is the game on striduel that is not solved by reasoning. No elimination will help you here: you aim, and the table answers. What you learn is a single rule — the angle of incidence equals the angle of reflection. Once you have it, you work a bank shot out in advance instead of trying it.
A game against the table takes three to five minutes. This is not tournament pool: no ball in hand, no obligation to hit a cushion. There is one call after all — but only in a duel, and only for the black.
The table
Twice as long as it is wide, with six pockets — four in the corners, two in the middle of the long sides. On it are eight balls: the cue ball, which is the one you shoot, and seven object balls, three of one colour, three of the other, and the black.
The two colours mean nothing in solo. They belong to the duel, which does not exist yet.
The rules
- Clear the table. All seven object balls count, and the black counts like any other: it does not have to go last, and you do not call a pocket.
- Your score is the number of shots. Fewer is better.
- A tie is broken by time — the same pattern as the puzzles. It is the second measure and not the first: taking your time to aim costs you nothing.
- There is no foul. You may hit any ball first, or none at all. Every shot costs one point, and that is the whole penalty.
- If the cue ball drops, it comes back to the break line — to its starting spot, or to the next free one behind it if that is taken. Balls already pocketed stay pocketed.
The shot
A shot is two numbers: an angle and a strength. No spin, no cue elevation. Learning angles does not need them, and they would double the physics.
It works like the hand on a cue: put your finger behind the cue ball and pull back. The direction runs from your finger through the ball and out the far side — you pull backwards, the shot goes forwards. The further back you pull, the harder it is; letting go plays the shot.
A short tap does nothing: under roughly sixteen screen pixels of pull, letting go has no effect at all. That is deliberate — every shot costs a point, and a slipped finger must not be one of them.
Two things sit alongside for fine work: the slider sets the strength exactly, and the ‹ › arrows turn the angle by two tenths of a degree each — finer than a finger on glass could ever land. That is what they are for: over a table this long, half a degree decides whether a ball drops.
The aiming aid
It is the heart of the learning and not a crutch, which is why it falls away as the setting goes up:
| Setting | What it shows |
|---|---|
| Easy | The cue ball's line up to the first contact, the spot where it stands there, and the direction the struck ball will take |
| Medium | Only a short ray at the cue ball: the direction, without the contact point |
| Hard | Nothing |
On no setting does it show you what happens. It stops at the first contact — a ball, a cushion, a pocket — and says nothing about what comes after. A line carried on past the cushion would not be learning any more, it would be reading off; the game would be solved instead of played.
Moving up a setting is therefore progress and not a loss: what the line used to show you, you now see for yourself.
Against a person
Billiards can also be played as a duel, by eight-ball rules. You create a duel and send the link; whoever opens it plays against you. Who breaks is drawn from the game's random value, so that it can be recomputed and does not depend on who clicked first.
Who owns which colour
At the start nobody owns a colour: the table is open, and either player may hit any ball first. Whoever pockets an object ball first takes that colour, and the other is the opponent's. If one ball of each colour falls in the same shot, the table stays open — that shot did not answer the question, and the next one asks it again.
Pocket one of your own and you shoot again. That is the whole reward mechanism of the game: a run does not come from collecting points but from your opponent never getting to the table.
Fouls, and why they are mild
A shot is a foul if you hit nothing, if you hit an opponent's ball first, or if you hit the black first while your own balls are still on the table. On an open table the second case cannot happen — there is no opponent's ball yet.
In all three the consequence is the same, and it is mild: the turn changes, and nothing else. No ball in hand, no extra shots, no points. Whatever fell during a foul stays down and counts for whoever owns it — even if you were the one who mishit.
If the cue ball drops, it returns to the break position and the turn changes. If that spot is taken, it moves to the next free one behind it.
The black, and the call
The black comes last. While you still have your own balls on the table you may not even hit it. Once they are gone, you call a pocket before the shot — that is an input of its own, not part of the shot.
| What happens | What follows |
|---|---|
| The black falls into the called pocket | Game won |
| The black falls into a different pocket | Game lost |
| The black does not fall | The turn changes, nothing else |
| The black falls and the cue ball with it | Game lost |
The second row is what makes the mode: a shot that sinks the black can win or lose the game — and which of the two is something you decide before you shoot. The last two pictures below show exactly that, from one and the same layout.
The clock
In a duel you have 30 seconds per shot. Go over and you lose. But they only start once your opponent's shot has finished playing out: while you are watching, your clock is not running. No clock is shown during that either — displaying a limit that has not started would be a display that hurries you and is wrong while it does.
Six shots, step by step
Six set-up positions, one shot each. Billiards has no solver that could suggest a shot — so the positions were picked, but every shot runs through the same physics that decides the game. What is drawn is what came back: the cue ball's path pale, the struck ball's path in colour, and the dashed circle is the spot where the cue ball stands at the moment of contact. The numbers under each table are worked out from those paths.
Shot 1Aim at the spot in front of the ball, not at the ball — The ball you hit leaves along the line through both centres — not along the line the cue ball came in on. Where the cue ball sits at the moment of contact is therefore the whole question; on the easy setting the aiming aid draws that spot as a pale circle, and here it is the dashed one. Angle 10.35°, strength 65%
Line of centres at contact 336.1° · path of the struck ball 336.1°
Shot 2The cushion mirrors the angle — This ball cannot be hit directly — another one stands in the line of sight. So it goes off the cushion: the cue ball runs in at a shallow angle and comes back out at the same one. That is the single rule this game teaches. Angle 325.30°, strength 80%
Angle to the cushion: in 34.7° · out 34.7°
Shot 3The struck ball mirrors it too — The rule belongs to the cushion, not to the cue ball. Here the object ball runs into the long side and from there into the corner pocket — a path that does not exist in a straight line. Once you see the angle, you see it everywhere on the table. Angle 320.15°, strength 85%
Angle to the cushion: in 54.2° · out 54.2°
Shot 4Where the cue ball goes afterwards — After the hit the two balls part at a right angle — every ball weighs the same, and that is all it takes. Here the object ball drops into the middle pocket, and that is exactly why the cue ball runs into the corner. A good shot with a bad ending: the cue ball comes back to the break line. Angle 4.65°, strength 80%
Between the paths of the two balls: 90.0°
Shot 5The black into the pocket you called — In a duel the black comes last, and whoever plays it calls a pocket first. Here that is the bottom-right corner, and in it goes: game won. Remember the layout — the next picture shows the same one. Angle 305.30°, strength 85%
The black falls into the pocket at (200 | 100) — the one that was called.
Shot 6Two point seven degrees off — Same layout, same strength, only the angle differs — and the black drops into the middle pocket instead of the corner. The corner was called, so this loses the game, not merely the turn. That is the whole difference between the two pictures, and it is smaller than the gap between two balls: from this one layout the black reaches four different pockets. The ‹ and › arrows adjust by 0.2° — thirteen taps lie between these two shots. Angle 308.00°, strength 85%
The black falls into the pocket at (100 | 100). 2.70° off the shot above, and so into the wrong one: game lost.
What actually helps
Three things are in the first four pictures, and together they are most of the game. Where the struck ball goes is decided by where the cue ball stands at contact. How a cushion answers is settled in advance — at the same angle you arrive at. And where the cue ball goes afterwards is not luck, it is the right angle to the ball you hit.
What no number will give you is the strength. Harder is not more accurate — a cushion swallows part of the speed at every contact, and a ball arriving too fast rattles past the pocket instead of into it.
Play it yourself
Billiards runs in the browser, no account needed. Start on easy and change setting as soon as you stop needing the line — that is the moment it exists for.