The Extra Card Fallacy

There seems to be this prevalent idea within the Magic community that you should never run 41 or 61 cards. The general claim is that running the extra card reduces your chances of drawing specific, important cards in your deck, and therefore is bad for your overall results. I intend to show that this claim, while it has some merit, is misleading. The fact of the matter is that there is a very good reason to run 61 cards in a deck that might otherwise want 60—mana ratio. The extra card provides a good way to control the number of lands you draw without giving up much in return. You can either run an extra land or an extra spell, and either raise or lower your mana ratio slightly.

The extra card does have an effect on your ability to draw any individual card in your deck (it would be weird if it didn't). However, this effect is much smaller than the effect it has on your ability to draw lands. In fact, the effect on your ability to draw lands is three to five times larger than the effect on your ability to draw any individual card.

Let's examine the data. The first order of business is to actually look at the effect an extra card has on your ability to draw any individual card. Here is the raw data:

% Chance of Drawing a Particular Card by a Particular Draw*

60 cards

* "Draw 0" is the opening hand.

Number of Copies in the Deck
1 copy2 copies3 copies4 copies5 copies6 copies7 copies8 copies
Draw 011.6722.1531.5439.9547.4654.1460.0965.36
Draw 113.3325.0835.4244.4852.4159.3365.3670.59
Draw 215.0027.9739.1448.7556.9964.0370.0275.11
Draw 316.6730.7942.7252.7761.2168.2674.1479.02
Draw 418.3333.5646.1656.5565.0972.0777.7682.37
Draw 520.0036.2749.4660.1068.6575.4980.9485.25
Draw 621.6738.9352.6263.4271.9178.5583.7287.71
Draw 723.3341.5355.6466.5474.9081.2986.1489.80
Draw 825.0044.0758.5369.4577.6383.7388.2591.58
Draw 926.6746.5561.3072.1680.1285.9090.0893.07
Draw 1028.3348.9863.9474.6982.3787.8291.6694.33
Draw 1130.0051.3666.4577.0584.4289.5293.0195.39
Draw 1231.6753.6768.8579.2386.2891.0294.1896.27
Draw 1333.3355.9371.1381.2687.9592.3395.1796.99
Draw 1435.0058.1473.2983.1389.4693.4896.0297.60
Draw 1536.6760.2875.3584.8690.8194.4996.7398.09
Draw 1638.3362.3777.2986.4692.0295.3697.3398.49
Draw 1740.0064.4179.1487.9293.1096.1197.8498.82
Draw 1841.6766.3880.8789.2694.0696.7698.2699.08
Draw 1943.3368.3182.5190.4994.9197.3198.6199.29
Draw 2045.0070.1784.0691.6195.6597.7998.8999.46


61 cards

Number of Copies in the Deck
1 copy2 copies3 copies4 copies5 copies6 copies7 copies8 copies
Draw 011.4821.8031.0839.4046.8453.4959.4164.67
Draw 113.1124.7034.9143.8951.7658.6564.6769.90
Draw 214.7527.5438.5948.1256.3163.3369.3374.45
Draw 316.3930.3342.1452.1160.5167.5773.4678.38
Draw 418.0333.0645.5455.8764.3971.3877.1081.77
Draw 519.6735.7448.8159.4067.9574.8280.3184.69
Draw 621.3138.3651.9462.7171.2277.9083.1287.19
Draw 722.9540.9354.9565.8274.2280.6685.5889.32
Draw 824.5943.4457.8268.7376.9683.1387.7391.14
Draw 926.2345.9060.5771.4579.4685.3389.6092.68
Draw 1027.8748.3163.2073.9981.7587.2991.2293.98
Draw 1129.5150.6665.7176.3583.8289.0292.6195.08
Draw 1231.1552.9568.1078.5585.7090.5593.8295.99
Draw 1332.7955.1970.3880.5987.4091.9094.8596.76
Draw 1434.4357.3872.5582.4988.9493.0995.7397.39
Draw 1536.0759.5174.6184.2490.3294.1296.4797.91
Draw 1637.7061.5876.5685.8691.5695.0397.1198.34
Draw 1739.3463.6178.4187.3492.6795.8197.6498.69
Draw 1840.9865.5780.1688.7193.6696.4998.0998.97
Draw 1942.6267.4981.8189.9794.5497.0898.4699.20
Draw 2044.2669.3483.3791.1195.3297.5898.7799.38



For the numerically challenged, here is a pretty picture:

Here is its effect on your mana ratio:

% Chance of Hitting Land Drops by Number of Lands

60 cards, on the play

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
20 lands95.1782.4263.7844.0527.2815.237.703.531.470.56
21 lands96.0284.9767.9848.9831.8918.8410.154.992.240.92
22 lands96.7387.2471.9053.8536.7122.8613.046.843.301.46
23 lands97.3389.2475.5358.6041.6727.2316.409.134.702.24
24 lands97.8490.9978.8763.1846.7131.9220.2111.886.493.30
25 lands98.2692.5181.9067.5451.7436.8524.4415.128.744.72
26 lands98.6193.8284.6371.6456.7041.9529.0518.8511.476.56
27 lands98.8994.9587.0675.4661.5447.1633.9823.0514.738.87
28 lands99.1395.9189.2178.9766.1852.3939.1727.6818.5111.71



60 cards, on the draw

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
20 lands96.9987.7572.2453.6435.8821.6811.865.892.651.08
21 lands97.6089.8376.1258.7541.2126.3015.308.133.941.75
22 lands98.0991.6279.6363.6546.6131.2719.2510.895.662.70
23 lands98.4993.1582.7968.2851.9936.5223.6814.197.864.03
24 lands98.8294.4585.5972.5957.2741.9528.5418.0410.605.79
25 lands99.0895.5488.0576.5662.3847.4833.7522.4113.908.06
26 lands99.2996.4590.1980.1767.2453.0239.2527.2717.7910.90
27 lands99.4697.2092.0383.4171.8158.4644.9232.5522.2514.34
28 lands99.5997.8293.6086.2976.0363.7150.6638.1727.2518.42


61 cards, on the play

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
20 lands94.8581.4962.3342.4325.8514.187.043.171.290.48
21 lands95.7384.0966.5347.2930.3017.609.304.491.980.80
22 lands96.4786.4270.4852.1034.9721.4112.006.172.921.27
23 lands97.1188.4874.1656.8139.8025.5815.148.264.171.95
24 lands97.6490.3077.5561.3844.7330.0718.7110.805.792.88
25 lands98.0991.8980.6565.7549.6834.8322.7013.797.824.14
26 lands98.4693.2683.4669.8954.5939.7827.0817.2610.315.77
27 lands98.7794.4585.9873.7759.4044.8631.8021.1913.297.85
28 lands99.0295.4788.2277.3664.0549.9936.7925.5616.7710.41


61 cards, on the draw

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
20 lands96.7686.9670.8551.9134.1920.3110.915.312.340.93
21 lands97.3989.1174.7856.9939.3824.7114.127.363.501.52
22 lands97.9190.9778.3661.8844.6629.4817.839.895.042.36
23 lands98.3492.5781.6066.5349.9634.5422.0112.947.033.53
24 lands98.6993.9484.4970.8955.1939.8126.6216.529.525.10
25 lands98.9795.0987.0474.9360.2945.2231.6220.6212.557.13
26 lands99.2096.0689.2878.6365.1750.6636.9125.2016.139.69
27 lands99.3896.8791.2281.9869.7956.0542.4130.2220.2812.82
28 lands99.5397.5492.8884.9774.0961.3048.0235.5924.9616.55



And some pretty pictures again:

To show some graphs that have less action, I have selected two common land counts, 24 and 27, and graphed the 60 vs. 61 card curves for those land counts:

I will now present the data for 40 and 41 cards, in the same format. First, the draw probabilities:

40 cards

1 Copy2 Copies3 Copies4 Copies5 Copies6 Copies
Draw 017.5032.3144.7855.2263.9371.14
Draw 120.0036.4149.8060.6569.4076.39
Draw 222.5040.3854.5065.5774.1880.82
Draw 325.0044.2358.9170.0178.3484.53
Draw 427.5047.9563.0274.0181.9587.62
Draw 530.0051.5466.8477.6085.0690.18
Draw 632.5055.0070.3980.8087.7392.29
Draw 735.0058.3373.6883.6490.0094.00
Draw 837.5061.5476.7286.1691.9395.39
Draw 940.0064.6279.5188.3793.5496.49
Draw 1042.5067.5682.0790.3194.8997.37
Draw 1145.0070.3884.4192.0096.0098.06
Draw 1247.5073.0886.5493.4596.9198.59
Draw 1350.0075.6488.4694.7097.6498.99
Draw 1452.5078.0890.1995.7698.2399.29
Draw 1555.0080.3891.7496.6598.7099.52



41 cards

1 Copy2 Copies3 Copies4 Copies5 Copies6 Copies
Draw 017.0731.5943.8654.2162.8770.09
Draw 119.5935.7348.9759.7668.5075.53
Draw 222.1039.7553.7564.7973.4280.12
Draw 324.6143.6458.2369.3377.7183.96
Draw 427.1247.3962.4173.4281.4287.17
Draw 529.6451.0266.2977.0984.6289.83
Draw 632.1554.5269.9180.3687.3792.01
Draw 734.6657.8973.2583.2789.7193.78
Draw 837.1861.1376.3485.8491.6995.22
Draw 939.6964.2479.1888.1193.3596.37
Draw 1042.2067.2281.7890.0994.7497.27
Draw 1144.7270.0784.1691.8195.8897.99
Draw 1247.2372.7986.3293.3096.8298.53
Draw 1349.7475.3888.2794.5897.5798.95
Draw 1452.2577.8490.0395.6698.1899.27
Draw 1554.7780.1891.6096.5898.6699.50



And, here we have a pretty picture again:

And, once again, here is the data for your land-drop probabilities:

40 cards, on the play

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
15 lands97.4289.2274.8656.8038.7423.6612.906.232.650.97
16 lands98.1491.8480.0364.0246.6830.9018.509.974.802.04
17 lands98.6993.9484.4670.6954.6338.7925.2214.948.033.88
18 lands99.0995.5988.1776.6862.3147.0632.8921.2012.546.77
19 lands99.3896.8691.2181.9069.5055.3841.2628.6418.4410.96
20 lands99.5897.8293.6386.3375.9963.4550.0037.0525.7216.66



40 cards, on the draw

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
15 lands98.5993.3282.6067.1249.5032.8919.5610.344.801.93
16 lands99.0495.2286.8973.9357.9641.5327.0315.878.343.88
17 lands99.3696.6590.3679.8765.9550.4335.4922.8413.367.04
18 lands99.5897.7193.1084.8973.2159.2044.5831.0919.9611.71
19 lands99.7498.4895.1988.9979.5867.4853.8840.2928.0518.08
20 lands99.8499.0296.7692.2484.9674.9762.9550.0037.3826.16



41 cards, on the play

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
15 lands97.0788.0472.7054.0235.9321.3411.285.282.160.76
16 lands97.8690.8278.0161.2043.5828.0816.318.513.961.62
17 lands98.4693.0782.6267.9351.3435.5222.4312.886.693.12
18 lands98.9194.8786.5474.0558.9443.4329.5218.4510.565.50
19 lands99.2496.2789.8079.4866.1751.5237.3825.1915.719.02
20 lands99.4897.3592.4584.1772.8259.5145.7432.9522.1713.88



41 cards, on the draw

Drop 1Drop 2Drop 3Drop 4Drop 5Drop 6Drop 7Drop 8Drop 9Drop 10
15 lands98.3692.4280.7164.3546.3529.9717.298.843.961.53
16 lands98.8794.4885.2271.2754.6638.1624.1213.716.963.12
17 lands99.2396.0688.9277.4162.6346.7431.9819.9511.285.73
18 lands99.4997.2591.8982.6870.0255.3540.5927.4717.069.66
19 lands99.6798.1294.2287.0976.6363.6449.5736.0324.3015.13
20 lands99.7998.7596.0090.6682.3371.3258.5345.2632.8322.22



And here are some more graphs:

Once again, I've selected common land counts—16, 17, 18—and graphed them independently.


Conclusion

The key here is to look at the spacing between the red and blue curves. It is evident that the extra card has a minimal effect on draw probabilities, especially past the first three or four draws. In fact, its effect is nearly always less than 1%. However, it is clear that by using the extra card, a player can gain extra resolution in their land-drop frequencies, allowing more fine-tuning for mana ratios. The effect of the extra card is in the 2% to 3% range for 60 cards, and the 3% to 5% range for 40 cards. If you don't use the potential of the extra card, you are left fine-tuning your mana ratios in larger increments. In fact, your ability to fine-tune is about half as good.

Now, let me ask you—do you lose more games to not drawing a specific card, or to drawing lands at the wrong time?

Chingsung Chang
Conelead most everywhere and on MTGO
Khan32k5 at gmail dot com