Chance of closing a run: how often you win twelve before losing three
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Both targets are fields, so this answers any format built as win so many before you lose so many. The starting numbers are the best known one, and nothing in the arithmetic is tied to it.
Results
| Runs you close, in per cent | — |
| Which is one run in | — |
| Wins the average run ends on | — |
| Runs ending with no wins, in per cent | — |
| Games the average run lasts | — |
The second row is the one that reframes the whole thing. A player who wins half of their games is not halfway to the target: they arrive once in about a hundred and fifty five attempts, and the typical attempt is over after three wins and six games.
Where the run actually ends
| Wins at the end | Chance of exactly that, in per cent | That many or fewer, in per cent |
|---|
The shape of that table is not the one people carry in their heads. The most likely place to finish is near the bottom rather than in the middle, one attempt in eight ends without a single win at an even win rate, and the pile of probability drains away long before the target.
The bold last row often sits higher than the row above it, and that is correct rather than a mistake. Finishing on the full target counts every run that got there with any number of losses to spare, while the row above it demands ending on the very last loss with exactly that many wins. One is a family of outcomes and the other is a single one.
What surprises most is how violently the top of the table answers to skill. Ten points of win rate do not add ten points to your chance of closing: they multiply it about six times over. The reason is that the target asks for a long string of wins against very few losses, so a dozen small advantages compound into one large one. The average run moves far less: those same ten points lift it by about half, while the chance of closing goes up six times over.
None of this knows anything about you beyond the one number you typed. It assumes every game is the same coin, which real runs are not: opponents get harder as you climb, and a deck that starts well can stop matching what it meets later. Treat the figure as the ceiling of a player with your average and no drift.
How often does an even player close the run?
Once in about a hundred and fifty five attempts, for twelve wins against three losses. Winning half your games does not put you halfway to the target, because the target is not asking for half.
The typical attempt is over quickly: three wins, six games. That is the run most people are actually having while they remember the rare long one.
| Win rate, in per cent | Runs closed, in per cent | One run in |
|---|---|---|
| 40 | 0,0609 | 1642,9 |
| 50 | 0,6470 | 154,6 |
| 60 | 3,9792 | 25,1 |
| 70 | 16,0836 | 6,2 |
| 80 | 44,8051 | 2,2 |
Why does a small change in win rate matter so much?
Because closing the run asks for a long string of wins against very few losses, and small advantages compound across every one of them. Ten points of win rate multiply the chance of closing about six times over.
The average run barely notices the same change, moving up by around half. The top of the distribution and the middle of it answer to skill on completely different scales, which is why two players with similar records can have very different memories of the format.
Why is the last row of the table higher than the one above it?
Because they are not the same kind of event. Finishing on the full target gathers every run that arrived with any number of losses left over, while the row above it demands ending on the final loss with exactly that many wins.
One is a family of outcomes and the other is a single one, so the family can easily be larger. It looks like a mistake in the chart and it is the arithmetic behaving correctly.
How many games does a run take?
Fewer than people plan for. At an even win rate the average is about six, because most runs end on the early losses rather than deep in the target.
That number rises with skill but slowly, since a better player plays more games per run precisely by not losing them. The page shows it next to the average wins so the two can be read together.
Does this apply to formats other than the famous one?
Yes, and that is why both targets are fields. Any format shaped as win so many before you lose so many uses the same arithmetic, whether that is a draft, a ladder event or a run in a game with no cards in it at all.
What the page cannot model is a win rate that changes as you go. Opponents get harder as you climb and a deck can stop matching what it meets, so treat the figure as the ceiling for a player with your average and no drift.
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