Magic: The Gathering / Lab / Draw odds
Draw odds
Seven cards off sixty, four copies of a name. A four-of is in your opening hand just under 40% of the time, and the mulligan does not change what you see, only what you keep.
31.5%
in your opening four — before any mulligan, either seat
| Turn | Cards seen | On the play | On the draw |
|---|---|---|---|
| 1 | 7 / 8 | 31.5% | 35.4% |
| 2 | 8 / 9 | 35.4% | 39.1% |
| 3 | 9 / 10 | 39.1% | 42.7% |
| 4 | 10 / 11 | 42.7% | 46.2% |
| 5 | 11 / 12 | 46.2% | 49.5% |
| 6 | 12 / 13 | 49.5% | 52.6% |
| 7 | 13 / 14 | 52.6% | 55.6% |
| 8 | 14 / 15 | 55.6% | 58.5% |
If you mulligan
53.1% of holding one after the mulligan, against 31.5% in the hand you are throwing back.
The whole hand is shuffled in and 7 are drawn again, so the second hand comes off a full deck and is independent of the first. ⚠ The chance of SEEING a copy is what improves here, and it costs one card to the bottom for each mulligan taken. You look at 7 either way, so mulliganing to find one card is buying a second look at the price of a card, not a better hand.
Every figure is a hypergeometric distribution evaluated exactly, not a simulation, so nothing here moves between page loads and any of it can be checked by hand. The rules it rests on are this game’s own: Rule 103.5 deals seven. Rule 100.2a is a sixty-card minimum and at most four of a name. Rule 103.8a is why the player going first is a card behind all game. Rule 103.5 again for the mulligan: a whole new seven, then one to the bottom per mulligan taken.