The cube

#What the cube does

The doubling cube is the second game being played on the board. At the start of a game it sits in the middle belonging to nobody, and the game is worth one point. Before you roll, you may turn it and offer your opponent a game at twice the stake. They answer in one of two ways: take, and the game goes on at the new stake with the cube now theirs alone to turn next, or pass, and you win what the game was worth before the offer.

That is the whole mechanism, and it is where most of the points in backgammon are won and lost. A game you play perfectly and cash for one point when it was worth four has cost you three, and nothing in the moves will show it.

The words this page uses, from anchor to market losers, are defined in the Glossary.

#Doubling, taking and passing

On your turn, before you roll, a Double button appears on your half of the board. Clicking the cube itself does the same thing.

When the cube is offered to you, Take and Pass appear instead, and the cube answers the mouse directly: left-click it to take, right-click it to pass.

Two things change that flow:

• Auto-roll skips the offer. With it on, your turn begins with the dice already thrown, which is what you want in a game you do not intend to double in and not what you want in one you do. See Playing.
• The Tutor watches the cube too. It grades four decisions, not one: a double, a double you did not make, a take and a pass. When the cube is the mistake it is the cube that changes colour rather than the dice, and under the full Tutor level a cube blunder is held before it happens, exactly as a checker blunder is. Under Hints a double you missed is mentioned after you have rolled, because by then the moment has passed and the coach is only saying what it would have done. See Playing.

The Crawford game has no cube at all, and the recap card says so before it starts. After the Crawford game the cube comes back, and see what the score does for why the trailer should then turn it almost immediately.

#Reading a cube decision

In an analysed match, the cube panel is the square icon in the detail toolbar, or press C to swap between it and the move list. Every cube turn has one, and so does every roll on which you were allowed to double.

The table has three rows:

The rows price lines, not verdicts. Double/Take is what the position is worth when the opponent accepts, so in a position they should pass it can read higher than No double without doubling being right. The line in words under the table is the answer: "Double, take", "No double, take", "Too good to double, pass". What each of the four verdicts means is in the Glossary.

Under that, the small ⓘ says what produced the numbers. A cube verdict depends on the model, on how deeply the cube was searched, on the currency, on the Jacoby rule and on the score, so two panels can answer one position differently and both be right. That token is where the difference is named.

A missed double is recorded against the roll you made instead. A player who should have doubled and rolled instead leaves no cube turn behind, so that turn carries two decisions: the play, graded as a circle, and the cube, graded as a square. One clean play made after failing to double is still a mistake, and Reading the analysis is where the symbols are.

The opening roll is the one exception: both players throw a single die and the winner plays that combination, so there is no moment in between at which the cube could have been offered, and no cube decision is scored there.

#Take point and cash point

Below the table sit the two edges of the doubling window.

• Take point is the share of the games the taker needs to win for taking to be better than passing, quoted in the taker's own winning chances, which is how take points are normally written.
• Cash point is the same threshold read from the doubler's side, so it is the one to compare against the win probability shown above the table.

Both come from the engine, at the cube efficiency and the score its own verdict used. That matters because the arithmetic a player learns for money is not the right arithmetic anywhere else: at a match score a take point is a ratio of match-equity differences, and it runs from a few percent to well past half, depending on what each side still needs.

approx. means the verdict searched. When the cube decision came from a search rather than from the formula, these two edges are a static reading of that search rather than its own break-even point. The search re-evaluates its own leaves and does not read the probabilities printed beside it, so a verdict can land the far side of a threshold shown here without either being wrong.

#When to double

The take point tells you whether a double can be accepted. It does not tell you whether to offer one, and that is the harder half.

The cube is worth something to whoever holds it, so a double gives away an asset as well as raising the stake. Turning it too early hands over that asset for a position that had not yet earned it. Waiting too long is the more expensive mistake, and the reason is market losers: the sequences after which your opponent would no longer have a take. A position with a lot of them is one where waiting often means having nothing left to offer that anybody would accept, and having to play on at one point a game you were winning at two.

So the question is not "am I ahead enough" but "can I still be doubling this next turn". Volatile positions, where a single exchange settles matters, are doubled earlier than quiet ones with the same winning chances.

At the other end, being much further ahead can make a double wrong again: the opponent would simply pass, and the gammons you were on course for go with the point you collected. That is the too good to double verdict, and the plan it names is to hold the cube, play on for the gammon, and turn it later only if the position starts to slip.

#Equity or match-winning chance

In match play the analysis carries an EQ / MWC toggle, over the cube panel and over the move list, and it starts on MWC.

MWC is the real currency of a match: your chance of winning the whole thing from here, and what a match analysis is made in. EQ is that same answer normalized into points, one game won being +1 and one lost -1, which is the scale money play is read on. Error rates and the blunder labels are normalized equity whichever you pick, so that a mistake near the end of a match and one at the start are measured on one scale. Money games have no match-winning chance to show, so the toggle is not there.

#What the score does

At a match score the cube is a different instrument. Points you cannot use are worth nothing, which changes both when a double is right and when it can be taken, sometimes drastically.

Three consequences worth knowing:

• At double match point the cube has nothing to do. Both sides win the match with the next game and gammons are worth nothing to either of them, so the game is a plain race for the win.
• The Crawford game has no cube, so that the trailer cannot double immediately with nothing to lose.
• After the Crawford game the trailer's cube is nearly free. The leader wins the match on any win, so turning the cube cannot increase what a loss costs. That makes doubling right at the first legal opportunity in almost every position, and the panel says Double even where it scores holding the cube exactly the same.

Two places in the app show the score's effect directly. In Study, a line under the verdict appears when the same position would get a different answer for money, and the Score matrix answers one position at every score, with a sensitivity figure saying the most you could lose by playing it as though the score were something else.

#How deeply the cube is searched

A cube decision can be reached two ways, and a server run lets you choose. Under Custom in the analysis run modal:

Formula applies Janowski's approximation to the probabilities the network returns, and costs almost nothing on top of the evaluation itself. Searched makes the cube a node in the search tree, so doubling, taking and playing on are each looked ahead a level, and Searched deep two. Searching is what gets a free cube and a marginal take right, and it is what a server run normally does.

Error currency is the other dial worth understanding, because it changes what every number in the match means and not just the cube ones. Cubeful prices a checker play in the currency that includes the cube, so a play that gets you doubled out is charged for it and one that cashes is paid for it. Cubeless ranks plays as though the game always played on. The two scales do not compare with each other.

While the cube decision searches, the numbers on the cube panel are searched at its depth rather than at the checker depth beside them, so they do not move when you re-run the checker analysis deeper. That is intended: what a cube panel shows is what its own verdict was reached from.