Schotten Totten Formation Statistics: Which Formations Win Stones?

What this study measures

This page is a data study, not a strategy guide. The odds of being dealt each formation are known and published. What nobody seems to have counted is the other side: once the cards are on the table, which formations actually win the stones? To find out, the site's AI played 400 games of the base game against itself, with the same playing strength on both sides and a fixed seed. Each time a stone was claimed we wrote down the claimant's formation, whether the opponent's side was still unfinished at that moment (a win by proof), and, when both sides were full, which formation lost.

These are the same 400 games behind our Schotten Totten tips, our Schotten Totten stone statistics and our Schotten Totten card value statistics. In all, the games produced 2,903 claims, about 7 per game. Stones still open when a game ended are not counted.

Two copies of one AI are not two people. They read the board the same way and never bluff, so read the figures as what careful, consistent play produces, not as a law of human play.

Which formation wins each stone

Rows follow the ladder, strongest first. Formation ladder: Schotten Totten rulebook, transcribed by RulesPal; figures: the site's game engine, base game, seed 20261011, the same AI on both sides, its search set to 200 iterations; in the base game it plays its heuristic move without running the search, so that setting has no effect.

Three of a kind leads clearly, with more than a third of all stones. The colour run comes second, ahead of the colour and well ahead of the run and the sum. With almost 3,000 claims, chance moves a row by a few dozen at most, and the four leading formations sit about 180 to 290 apart, so that order is solid. The run and the sum are only 51 apart, about twice the typical chance swing: the run probably wins a little more often, but a rerun could narrow that gap.

Rare to deal, common to win

The ladder ranks formations by how rare they are in a deal, and the colour run is the rarest of all. The exact counts are on our page of Schotten Totten formations ranked by rarity. Yet in play it wins a quarter of the stones, more than the colour, which is far more common in a deal.

The reason is that nobody waits to be dealt a formation. A player lays two cards of a run in one colour on a stone and waits for the third. The numbers suggest the AI plays this way often, and with reason: a finished colour run is almost impossible to beat. The deal decides what you start with. The table decides what you finish with, and players steer towards the top of the ladder.

The plain sum is the mirror case. Any three cards make a sum, so it is the most common thing to hold, but it wins only about one stone in ten. A sum is what you finish with when the plan for a stronger formation failed.

Won by proof or head to head

A stone can be claimed before the opponent has finished their side, if no card they could still get would let them beat you. In this study we call that a win by proof (once both sides are full, the proof is just a comparison), and how to run it is explained in how to claim a stone in Schotten Totten. In our games, 937 claims out of 2,903, about one in three, were won that way.

The share depends on the formation. About 42% of colour wins came by proof, 37% of three-of-a-kind wins and 32% of colour-run wins. The run follows at 27%, and the sum falls to 4%: 11 wins out of 299. A sum is easy to beat while the opponent still has a card to add, so it can rarely be proved early. It has to wait for the other side to fill up and lose.

What the losing line looks like

In the 1,966 claims decided head to head, both sides were full, so we can see what lost:

More than half of the losing lines, 53%, were a plain sum. Only 31 colour runs were ever beaten head to head, each time by another colour run. In 534 of these stones, 27%, both sides held the same formation, and the card total or the side that finished first decided the stone.

When a sum won, the total ranged from 8 to 26, with a median of 19. Of the 299 winning sums, 131 were 20 or more and 72 were 15 or less. A low sum can still take a stone, but only against a line that is no stronger.

What it changes at the table

Three practical readings, in order of confidence.

First, aim high early. Most stones are won by three of a kind or a colour run, and most losing lines are sums. A side that drifts into a sum is usually a side that loses. Start each stone with two cards that can still become a strong formation.

Second, the colour run is not a lottery ticket. It is rare in a deal, but common on the board, because you build it. Two cards of a run in one colour, with the third still unseen, is a real plan. Check that the cards you need are still unseen before you commit.

Third, a strong formation finished early can be claimed early. A third of all claimed stones were won by proof before the opponent finished, nearly nine in ten of them with a formation above the run. For the full picture of how to win a game, read the Schotten Totten rules first and then the Schotten Totten strategy guides.