Why Multiplicative Scoring Changes Everything

Jelmata looks like a territory game. You place cells, your opponent places cells, whoever has more points at the end wins. Familiar enough. But there's one line in the scoring rule that bends the whole game away from Go, Othello, Reversi, and every majority game you've ever played: your score is the product of your connected-component sizes, not the sum. Six cells on the board can be worth 6 points, or 9, or 36, depending entirely on how those cells are grouped. This post is about what that rule actually does to the game once you take it seriously.

Imagine you have exactly six of your cells on the board. In a territory game, that's six points. Always. It doesn't matter whether they're huddled together or scattered across corners — a stone is a stone.

In Jelmata, those same six cells can be worth anywhere from 1 to 9 points, depending only on how they partition into groups:

Same six cells. A 9x swing between the best and worst arrangement. That table is the entire game in miniature — the winner isn't whoever has the most cells, it's whoever arranged their cells into the best partition.

Look at the table again. Notice the pattern: the highest scores come from splitting roughly evenly, and the lowest come from extremes. There's a reason for that, and it's a classical inequality you may not have met by name — the arithmetic-geometric mean inequality. In one sentence, and without any formulas: for a fixed sum, the product of several numbers is largest when those numbers are as equal as possible.

That's why 3 × 3 = 9 beats 5 × 1 = 5 and 4 × 2 = 8. Doubling down on a big group costs you more than the small group gives back. The math rewards balance.

But there's a catch: a group of one multiplies your score by one, which is to say it does nothing. Singletons are almost worthless. So the real sweet spot isn't “split as much as possible” — it's several medium-sized groups with nothing left over. On a 5×5 board, ten cells arranged as 3 + 3 + 2 + 2 score 36. The same ten cells dumped into a single 2×5 block score 10. More than three and a half times the payoff, for exactly the same investment of moves.

Four green groups — two threes and two twos — anchored in the corners. Score = 3 × 3 × 2 × 2 = 36.

Exact same ten cells, welded into one block across the middle rows. Score = 10. Everything that made the first position powerful has been collapsed into a single factor.

This is where multiplicative scoring stops being a curiosity and starts hurting. In an additive game, every piece you place is worth roughly +1 to your score. Place a stone, add a point. The only question is where to put it. In Jelmata, a placed cell can be worth a lot, a little, nothing — or a negative amount. A single move can make your score go down.

There are three things a move can do, and they have wildly different values:

• Grow a group. You add a cell to an existing group of 4. That factor goes from 4 to 5, multiplied by everything else. Nice.
• Start a new group. You place a cell with no friendly neighbors. You've created a group of 1, which multiplies your score by 1. You gained nothing — yet. The hope is that this seedling becomes a group of 3 or 4 later.
• Merge two groups. You place a cell between two of your own groups. Their factors collapse into one, and the new factor is usually smaller than the old factors multiplied. This is the merge tax.

Green has two groups of 4. Score = 4 × 4 = 16. The marked center cell is adjacent to a cell in each group, so playing there fuses them into one 9-cell component. New score = 9. The move is worth −7. In Go, that same move would be worth +1 and nobody would think twice about it. In Jelmata it's a disaster you have to actively see coming.

The merge tax is the single biggest reason Jelmata rewards a kind of careful, spatial thinking that territory games don't demand. In Go you're asking “is this square mine or theirs.” In Jelmata you're asking “if I put a cell here, does it connect two factors that were supposed to stay separate.”

If you're coming from Go, Othello, Reversi, or most other grid-and-stones games, a few well-practiced habits are going to quietly cost you points in Jelmata until you rewire them. The patterns below feel right in additive games and feel wrong in a multiplicative one.

• “Build a big connected wall.” In Go a wall projects influence. In Jelmata a wall is one component, collapsing a sum of factors into a single factor. The bigger the wall, the more painful the collapse.
• “The center is the most valuable real estate.” In Othello, center control is decisive. In Jelmata, interior cells have four neighbors — the maximum number of ways for a move to accidentally bridge two of your own groups. The center is the highest merge-risk square on the board.
• “More stones means more points.” Only if those stones were arranged well. A player with ten cells in one blob scores 10. A player with eight cells in two groups of 4 scores 16. Cell count and score are genuinely different quantities.
• “Sacrifices are about tempo.” In Jelmata, the main “sacrifice” you make is accepting a merge you can't prevent, because the alternative is letting your opponent grow a bigger factor somewhere else. The currency you're trading isn't time — it's factorization.

Once you internalize the product rule, a lot of Jelmata's strategy falls out as corollaries rather than separate tips. Play the perimeter — because corners and edges have fewer neighbors, and fewer neighbors means fewer chances to trigger a merge tax. Split into multiple medium groups — because AM-GM says balance wins. Be suspicious of any move that touches two of your own groups — because it probably has a negative score delta even though it increases your cell count.

This is also, incidentally, why Jelmata's AI works the way it does. The Hard and Elite models were trained from scratch with self-play — no human games, no opening theory, no rules about corners. After a few thousand games they independently learned one of the strongest negative weights in the entire model: a penalty for playing in the center. Nobody told them about the merge tax. They discovered it the same way you will — by losing games to it first.

If you want the tactical corollary in visual form, read the companion post Strategy Tips: Play the Perimeter — it takes the theory on this page and turns it into the moves you actually make. And then the best thing to do is close the browser tab and play a game, because the fastest way to feel the product rule is to watch your score drop by seven from a single innocent-looking move.