Mulligan Math...

Mulligan Math - What are the Odds? (Revised)

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You’ve just finished drafting your Arena deck, and though there are some solid cards in there, the mana curve is steeper than Mount Fuji (I live in Japan). You press “Play” and, as expected, all three starting cards cost 4 or more mana. Do you keep a 4-drop, just in case? Well, that all depends on how lucky you’re feeling. Below are the chances you get what you want

REVISION FROM THE AUTHOR: A few weeks ago, I had published this article, however Among the comments there were those who felt it would be more useful to include the first card drawn after the mulligan when calculating the odds. I happen to agree, and so here are the revised odds!

  • M = number of cards you choose to mulligan
  • # = number of desired cards in your deck
  • Get # = the chance you get at least that number of desired cards)

Good luck, and happy mulligan-ing!

Going First

Going Second
M # Get 1 Get 2 Get 3 Get 4
0 1 3.7% 0% 0% 0%
0 2 7.4% 0% 0% 0%
0 3 11.1% 0% 0% 0%
0 4 14.8% 0% 0% 0%
0 5 18.5% 0% 0% 0%
0 6 22.2% 0% 0% 0%
0 7 25.9% 0% 0% 0%
0 8 29.6% 0% 0% 0%
0 9 33.3% 0% 0% 0%
0 10 37% 0% 0% 0%
0 11 40.7% 0% 0% 0%
0 12 44.4% 0% 0% 0%
0 13 48.1% 0% 0% 0%
0 14 51.9% 0% 0% 0%
0 15 55.6% 0% 0% 0%
0 16 59.3% 0% 0% 0%
0 17 63% 0% 0% 0%
0 18 66.7% 0% 0% 0%
0 19 70.4% 0% 0% 0%
0 20 74.1% 0% 0% 0%
0 21 77.8% 0% 0% 0%
0 22 81.5% 0% 0% 0%
0 23 85.2% 0% 0% 0%
0 24 88.9% 0% 0% 0%
0 25 92.6% 0% 0% 0%
0 26 96.3% 0% 0% 0%
0 27 100% 0% 0% 0%
1 1 7.3% 0% 0% 0%
1 2 14.3% 0.3% 0% 0%
1 3 21% 0.8% 0% 0%
1 4 27.4% 1.6% 0% 0%
1 5 33.6% 2.7% 0% 0%
1 6 39.5% 4.1% 0% 0%
1 7 45.1% 5.8% 0% 0%
1 8 50.5% 7.7% 0% 0%
1 9 55.6% 9.9% 0% 0%
1 10 60.4% 12.3% 0% 0%
1 11 64.9% 15.1% 0% 0%
1 12 69.1% 18.1% 0% 0%
1 13 73.1% 21.4% 0% 0%
1 14 76.8% 25% 0% 0%
1 15 80.2% 28.8% 0% 0%
1 16 83.4% 32.9% 0% 0%
1 17 86.3% 37.3% 0% 0%
1 18 88.9% 42% 0% 0%
1 19 91.2% 46.9% 0% 0%
1 20 93.3% 52.1% 0% 0%
1 21 95.1% 57.6% 0% 0%
1 22 96.6% 63.4% 0% 0%
1 23 97.8% 69.4% 0% 0%
1 24 98.8% 75.7% 0% 0%
1 25 99.5% 82.3% 0% 0%
1 26 99.9% 89.2% 0% 0%
1 27 100% 96.3% 0% 0%
2 1 10.8% 0% 0% 0%
2 2 20.9% 0.8% 0% 0%
2 3 30.1% 2.4% 0% 0%
2 4 38.6% 4.6% 0.1% 0%
2 5 46.4% 7.5% 0.3% 0%
2 6 53.5% 10.9% 0.6% 0%
2 7 59.9% 14.8% 1.1% 0%
2 8 65.7% 19.2% 1.8% 0%
2 9 70.9% 23.9% 2.7% 0%
2 10 75.6% 29% 3.8% 0%
2 11 79.7% 34.2% 5.2% 0%
2 12 83.4% 39.7% 7% 0%
2 13 86.6% 45.3% 9.1% 0%
2 14 89.3% 50.9% 11.5% 0%
2 15 91.6% 56.5% 14.4% 0%
2 16 93.6% 62% 17.7% 0%
2 17 95.3% 67.4% 21.5% 0%
2 18 96.6% 72.6% 25.8% 0%
2 19 97.6% 77.6% 30.7% 0%
2 20 98.4% 82.2% 36.1% 0%
2 21 99.1% 86.4% 42.1% 0%
2 22 99.5% 90.2% 48.7% 0%
2 23 99.7% 93.4% 56.1% 0%
2 24 99.9% 96.1% 64.1% 0%
2 25 100% 98.1% 72.8% 0%
2 26 100% 99.5% 82.3% 0%
2 27 100% 100% 92.6% 0%
3 1 14.4% 0% 0% 0%
3 2 27.2% 1.6% 0% 0%
3 3 38.5% 4.6% 0.1% 0%
3 4 48.4% 8.7% 0.5% 0%
3 5 57.1% 13.7% 1.2% 0%
3 6 64.6% 19.4% 2.3% 0.1%
3 7 71.1% 25.7% 3.9% 0.2%
3 8 76.7% 32.2% 6% 0.4%
3 9 81.4% 39% 8.6% 0.6%
3 10 85.4% 45.8% 11.9% 1.1%
3 11 88.7% 52.4% 15.7% 1.7%
3 12 91.4% 58.9% 20.1% 2.5%
3 13 93.5% 65.1% 25% 3.6%
3 14 95.3% 70.9% 30.4% 5.1%
3 15 96.7% 76.2% 36.3% 6.9%
3 16 97.7% 81% 42.5% 9.2%
3 17 98.5% 85.2% 49.1% 12.1%
3 18 99% 88.9% 55.8% 15.5%
3 19 99.4% 92% 62.6% 19.6%
3 20 99.7% 94.5% 69.3% 24.5%
3 21 99.8% 96.5% 75.8% 30.3%
3 22 99.9% 98% 81.9% 37%
3 23 100% 99% 87.5% 44.8%
3 24 100% 99.6% 92.3% 53.8%
3 25 100% 99.9% 96.1% 64.1%
3 26 100% 100% 98.8% 75.7%
3 27 100% 100% 100% 88.9%
M # Get 1 Get 2 Get 3 Get 4 Get 5
0 1 3.8% 0% 0% 0% 0%
0 2 7.7% 0% 0% 0% 0%
0 3 11.5% 0% 0% 0% 0%
0 4 15.4% 0% 0% 0% 0%
0 5 19.2% 0% 0% 0% 0%
0 6 23.1% 0% 0% 0% 0%
0 7 26.9% 0% 0% 0% 0%
0 8 30.8% 0% 0% 0% 0%
0 9 34.6% 0% 0% 0% 0%
0 10 38.5% 0% 0% 0% 0%
0 11 42.3% 0% 0% 0% 0%
0 12 46.2% 0% 0% 0% 0%
0 13 50% 0% 0% 0% 0%
0 14 53.8% 0% 0% 0% 0%
0 15 57.7% 0% 0% 0% 0%
0 16 61.5% 0% 0% 0% 0%
0 17 65.4% 0% 0% 0% 0%
0 18 69.2% 0% 0% 0% 0%
0 19 73.1% 0% 0% 0% 0%
0 20 76.9% 0% 0% 0% 0%
0 21 80.8% 0% 0% 0% 0%
0 22 84.6% 0% 0% 0% 0%
0 23 88.5% 0% 0% 0% 0%
0 24 92.3% 0% 0% 0% 0%
0 25 96.2% 0% 0% 0% 0%
0 26 100% 0% 0% 0% 0%
1 1 7.5% 0% 0% 0% 0%
1 2 14.8% 0.3% 0% 0% 0%
1 3 21.7% 0.9% 0% 0% 0%
1 4 28.4% 1.8% 0% 0% 0%
1 5 34.8% 3% 0% 0% 0%
1 6 40.8% 4.4% 0% 0% 0%
1 7 46.6% 6.2% 0% 0% 0%
1 8 52.1% 8.3% 0% 0% 0%
1 9 57.2% 10.7% 0% 0% 0%
1 10 62.1% 13.3% 0% 0% 0%
1 11 66.7% 16.3% 0% 0% 0%
1 12 71% 19.5% 0% 0% 0%
1 13 75% 23.1% 0% 0% 0%
1 14 78.7% 26.9% 0% 0% 0%
1 15 82.1% 31.1% 0% 0% 0%
1 16 85.2% 35.5% 0% 0% 0%
1 17 88% 40.2% 0% 0% 0%
1 18 90.5% 45.3% 0% 0% 0%
1 19 92.8% 50.6% 0% 0% 0%
1 20 94.7% 56.2% 0% 0% 0%
1 21 96.3% 62.1% 0% 0% 0%
1 22 97.6% 68.3% 0% 0% 0%
1 23 98.7% 74.9% 0% 0% 0%
1 24 99.4% 81.7% 0% 0% 0%
1 25 99.9% 88.8% 0% 0% 0%
1 26 100% 96.2% 0% 0% 0%
2 1 11.2% 0% 0% 0% 0%
2 2 21.6% 0.9% 0% 0% 0%
2 3 31.1% 2.6% 0% 0% 0%
2 4 39.9% 5% 0.1% 0% 0%
2 5 47.8% 8% 0.4% 0% 0%
2 6 55% 11.7% 0.7% 0% 0%
2 7 61.6% 15.9% 1.2% 0% 0%
2 8 67.4% 20.5% 2% 0% 0%
2 9 72.6% 25.6% 3% 0% 0%
2 10 77.3% 30.9% 4.3% 0% 0%
2 11 81.4% 36.4% 5.9% 0% 0%
2 12 84.9% 42.2% 7.8% 0% 0%
2 13 88% 48% 10.2% 0% 0%
2 14 90.6% 53.8% 12.9% 0% 0%
2 15 92.8% 59.6% 16.2% 0% 0%
2 16 94.7% 65.3% 19.9% 0% 0%
2 17 96.2% 70.8% 24.1% 0% 0%
2 18 97.3% 76% 29% 0% 0%
2 19 98.3% 80.9% 34.4% 0% 0%
2 20 98.9% 85.4% 40.5% 0% 0%
2 21 99.4% 89.5% 47.2% 0% 0%
2 22 99.7% 92.9% 54.7% 0% 0%
2 23 99.9% 95.8% 62.9% 0% 0%
2 24 100% 98% 71.9% 0% 0%
2 25 100% 99.4% 81.7% 0% 0%
2 26 100% 100% 92.3% 0% 0%
3 1 14.9% 0% 0% 0% 0%
3 2 28.1% 1.7% 0% 0% 0%
3 3 39.7% 4.9% 0.1% 0% 0%
3 4 49.9% 9.3% 0.5% 0% 0%
3 5 58.7% 14.7% 1.3% 0% 0%
3 6 66.3% 20.7% 2.5% 0.1% 0%
3 7 72.8% 27.3% 4.3% 0.2% 0%
3 8 78.3% 34.2% 6.6% 0.4% 0%
3 9 82.9% 41.3% 9.6% 0.7% 0%
3 10 86.7% 48.3% 13.1% 1.2% 0%
3 11 89.9% 55.2% 17.3% 2% 0%
3 12 92.5% 61.8% 22.1% 2.9% 0%
3 13 94.5% 68% 27.5% 4.2% 0%
3 14 96.1% 73.8% 33.4% 5.9% 0%
3 15 97.3% 79% 39.7% 8.1% 0%
3 16 98.2% 83.7% 46.4% 10.8% 0%
3 17 98.9% 87.7% 53.3% 14.1% 0%
3 18 99.3% 91.1% 60.4% 18.1% 0%
3 19 99.6% 93.9% 67.4% 22.9% 0%
3 20 99.8% 96.1% 74.2% 28.7% 0%
3 21 99.9% 97.8% 80.7% 35.4% 0%
3 22 100% 98.9% 86.6% 43.3% 0%
3 23 100% 99.6% 91.7% 52.4% 0%
3 24 100% 99.9% 95.8% 62.9% 0%
3 25 100% 100% 98.7% 74.9% 0%
3 26 100% 100% 100% 88.5% 0%
4 1 18.6% 0% 0% 0% 0%
4 2 34.4% 2.9% 0% 0% 0%
4 3 47.6% 8% 0.3% 0% 0%
4 4 58.6% 14.6% 1.3% 0% 0%
4 5 67.7% 22.3% 3.1% 0.1% 0%
4 6 75.1% 30.6% 5.7% 0.4% 0%
4 7 81.1% 39.2% 9.3% 0.9% 0%
4 8 85.8% 47.6% 13.8% 1.8% 0.1%
4 9 89.6% 55.7% 19.2% 3% 0.2%
4 10 92.5% 63.3% 25.4% 4.9% 0.3%
4 11 94.7% 70.3% 32.1% 7.3% 0.6%
4 12 96.4% 76.4% 39.4% 10.4% 1%
4 13 97.6% 81.8% 46.9% 14.3% 1.7%
4 14 98.5% 86.4% 54.5% 19.1% 2.6%
4 15 99.1% 90.2% 61.9% 24.6% 3.9%
4 16 99.5% 93.2% 69.1% 30.9% 5.6%
4 17 99.7% 95.5% 75.7% 38% 8%
4 18 99.9% 97.2% 81.8% 45.7% 11%
4 19 99.9% 98.4% 87% 53.8% 15%
4 20 100% 99.2% 91.4% 62.3% 19.9%
4 21 100% 99.6% 94.8% 70.8% 26.2%
4 22 100% 99.9% 97.3% 79% 33.9%
4 23 100% 100% 98.9% 86.6% 43.3%
4 24 100% 100% 99.7% 92.9% 54.7%
4 25 100% 100% 100% 97.6% 68.3%
4 26 100% 100% 100% 100% 84.6%

 

 

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