After the deal with three players, 28.5% of players hold at least one marriage, a player is dealt four nines in 0.33% of deals, and in the games of our bots under house rules one game lasts on average 25.2 deals. Below are all the numbers and where they come from.
How we counted
The probabilities we calculated exactly — by counting all the possible arrangements of the cards, with no random samples. The simulation we ran on the engine of our game: whole games were played by bots.
Marriages
| How many cards | At least one | Hearts marriage | Average number of marriages | Average points from marriages |
|---|---|---|---|---|
| 3 (the kitty, musik in Polish) | 4.3% | 1.1% | 0.04 | 3.04 |
| 7 (a hand with three players) | 28.5% | 7.6% | 0.30 | 21.30 |
| 10 (with the kitty, or with two players) | 54.0% | 16.3% | 0.65 | 45.65 |
| 12 (two players, with the kitty) | 70.4% | 23.9% | 0.96 | 66.96 |
More about marriages: marriages.
Four nines
A player dealt 7 cards has four nines in 0.33% of deals — once in 304. With 10 cards (two players) it is 1.98%, that is once in 51. The figures concern the hand of one player; the chance that anyone at the table is dealt four nines is correspondingly greater.
How long a game lasts
| Rules | Players | Deals per game | Contracts made (without bombs) | Average contract | Bombs per game |
|---|---|---|---|---|---|
| house | 2 | 16.1 | 81.2% | 108 | 1.7 |
| house | 3 | 25.2 | 67.8% | 104 | 5.3 |
| house | 4 | 30.4 | 68.9% | 104 | 6.8 |
| tournament | 2 | 17.6 | 73.0% | 108 | 0.0 |
| tournament | 3 | 32.2 | 53.8% | 104 | 0.0 |
| tournament | 4 | 38.8 | 53.7% | 104 | 0.0 |
Each row is 2,000 games played by bots. “Contracts made (without bombs)” is the share of deals played to the end — without those ended by a bomb — in which the declarer made the contract; “average contract” is the typical contract across all deals, also those ended by a bomb. Under house rules the bots throw a bomb with weak cards, so they play to the end mainly the better deals — hence the higher share of contracts made than under tournament rules, where there is no bomb. The rules of both variants: scoring.
How to cite
Thousand (1000), “Thousand statistics”, as of 8 October 2026 — with the address of this page.