The ranking is a rarity count, not an opinion
A stone goes to the stronger three-card formation, on this ladder:
colour run > three of a kind > colour > run > sum
Card players stall on one rung: three of a kind beats a colour (flush). In a poker deck that is backwards. But Schotten Totten's deck is only 54 cards — values 1 to 9 in six colours, each value once per colour — and in that deck the ranking is exactly the order of how few of each formation exist. Rarer beats commoner, and the numbers below prove it.
The exact numbers
Out of every possible three-card group in the deck:
| Formation | How many exist | Why |
|---|---|---|
| Colour run | 42 | 7 runs (1-2-3 … 7-8-9) × 6 colours |
| Three of a kind | 180 | 9 values × the 20 ways to pick 3 of 6 colours |
| Colour | 462 | 84 same-colour triples per colour, minus the 7 runs, × 6 |
| Run | 1,470 | 7 value-runs × 210 non-single-colour colourings |
| Sum | everything else | far more numerous — which is why it is weakest |
A colour run is thirty-five times rarer than a plain run, and over five hundred times rarer than a bare sum hand. That gap is the whole reason the ladder feels so decisive: when you complete a colour run, almost nothing in the deck beats it.
Completion odds — the number that actually matters
Rarity ranks a finished formation. What wins games is knowing your odds of finishing the one you started, from two cards down with one to go.
The gap is brutal. A budding colour run — say blue 5, blue 6 — completes on only blue 4 or blue 7: two cards in the whole deck. A plain run, blue 5 and red 6, completes on any 4 or any 7: up to twelve cards. Same shape on the board, six times the outs.
The tool below counts live outs for any two cards you place. The habit it should build: before you commit a third card to a premium formation, count the cards that finish it, then subtract the ones you can already see. Two outs is a gamble; ten is a plan.
Assumes only your two placed cards are visible (pool of 52). Every card you actually see shrinks the pool and sharpens the count.
Playing the odds
Three habits fall straight out of the counts:
- Bank the sure thing. A completed colour or three-of-a-kind is already top-5% rare; don't break it chasing a run that needs two exact cards.
- Bluff with the rare tiers. Two same-colour consecutive cards threaten a colour run even if you never draw it — your opponent must respect the 42-in-the-deck monster.
- Win ties by finishing early. Between equal formations the higher total wins, then whoever completed first. On a sum or colour where you might tie, playing your third card a turn sooner can take the stone outright.
The odds in five lines
- The formation ladder is a rarity ranking: colour run (42) > three of a kind (180) > colour (462) > run (1,470) > sum.
- Three of a kind really beats a colour — in a 54-card deck it is rarer.
- A colour run is ~35× rarer than a plain run and hundreds of times rarer than a sum hand.
- Completion is what matters mid-hand: a colour-run draw has ~2 outs, a plain run up to ~12.
- Count your outs before committing a third card; bank rare finished formations; bluff with same-colour pairs.
Frequently asked questions
What is the best hand in Schotten Totten?
A colour run — three consecutive values in one colour (e.g. blue 5-6-7). Only 42 exist in the deck, making it the rarest and strongest formation. The highest possible is the 7-8-9 colour run.
What are the odds of a straight flush (colour run)?
There are exactly 42 colour runs among all three-card groups in the 54-card deck — 7 runs per colour × 6 colours. Mid-hand, a two-card colour-run draw usually has just two outs, so completing one you did not start with is genuinely hard.
Why does three of a kind beat a flush here?
Because the deck has only six of each value. Three of a kind (180 possible) is rarer than a colour (462 possible), and Schotten Totten ranks formations by rarity, so three of a kind sits above colour.
How many of each formation are there?
Colour run 42, three of a kind 180, colour 462, run 1,470, and every remaining three-card group scores as a sum. The ranking follows those counts exactly.