Order of Operations, Explained Properly

If you have ever built an equation that looked right and evaluated to something else entirely, this is almost always why. The rules are short, and once they click they stop costing you solves.

The order, in the order

Every equation in 37 is evaluated by the same rules used in mathematics everywhere. They resolve in this sequence:

Parentheses — anything inside brackets, innermost first.
Exponents — powers, before any multiplying or dividing.
Multiplication and division — together, left to right.
Addition and subtraction — together, left to right.

You may have learned this as PEMDAS, BODMAS or BIDMAS. They are the same rules with different initials.

The two that actually bite

Multiplication does not come before division

The "M" sitting before the "D" in PEMDAS misleads almost everyone. Multiplication and division sit at the same level of precedence and resolve left to right. So 12/2*3 is (12/2)*3 = 18, not 12/(2*3) = 2. The same is true of addition and subtraction: 10-3+2 is 9, not 5.

Exponents beat multiplication

A power binds tighter than a product. In 3*3^2, the square happens first: 3*9 = 27, not 9^2 = 81. This matters constantly in 37 because the red power die is an exponent die, and players routinely expect it to apply to a whole term when it only applies to the number it touches.

3×6+1+3+3^2+6 3×6 = 18, and 3² = 9 resolves on its own before anything is added. 18+1+3+9+6 = 37.

Parentheses are how you overrule the rules

Brackets exist precisely so you can force an order the default precedence would not give you. If you want a sum multiplied, the sum has to be in brackets — 2+3*4 is 14, whereas (2+3)*4 is 20.

In practice this is the single most powerful tool on the board, because it is how you turn several small dice into one useful number.

(6+3)×4+4−2−5÷5 The bracket makes 9, which multiplies to 36. Then +4−2 = +2, and 5/5 = 1 is subtracted. 36+2−1 = 37.

Read that last one carefully: 5/5 resolves before the subtraction, because division outranks subtraction. You are subtracting 1, not dividing the running total.

Evaluating an equation step by step

The reliable way to check your own work is to resolve an equation in passes, exactly as the game engine does — one precedence level at a time, left to right within each level. Take (6+3)*4+4-2-5/5:

Parentheses. (6+3) becomes 9. The equation is now 9*4+4-2-5/5.
Exponents. There are none here, so nothing changes.
Multiplication and division, left to right. 9*4 becomes 36, then 5/5 becomes 1. The equation is now 36+4-2-1.
Addition and subtraction, left to right. 36+4 is 40, minus 2 is 38, minus 1 is 37.

Doing it in this order takes about five seconds and removes essentially all precedence errors. The mistake people make is evaluating strictly left to right in one pass — which would give (6+3)*4 = 36, then +4 = 40, then −2 = 38, then −5 = 33, then ÷5 = 6.6. Same symbols, wildly different answer.

It is also worth knowing that division can produce fractions mid-equation. There is nothing wrong with that as long as the final total is exactly 37 — but an equation that passes through 6.6 and comes back to a whole number is usually a sign you have mis-grouped something.

A quick self-test

Work these out before reading the answers. If you get all four, precedence will never cost you a solve again.

2+3*4 — is it 20 or 14?
12/2*3 — is it 2 or 18?
2*3^2 — is it 36 or 18?
10-3+2 — is it 5 or 9?

Answers

14, 18, 18, 9. Every one of them is the second option — which is the point: the intuitive reading is usually the wrong one.

If a solve is still evaluating unexpectedly, the culprit is almost always an exponent binding tighter than you assumed. The exponent guide covers that case in detail.