Mathhammer for the Hive Mind

I actually enjoy doing mathematical analysis to see how efficient different units are. Dice can be fickle but the more dice you roll should bring you closer to the mean. Not that this helps my constantly under-performing Tervigon. This page is intended as a mathematical reference for Tyranid players and I shall be adding more analysis (and formatting) later.


Calculus for Hive Tyrants
Pythagoras' Theorem will help with guessing ranges but beyond that maths will not win you games. What it will do is help you to know what performance to expect from your army. Of course knowing that your Hive Guard should kill three Rhinos in a six turn game does not help if they underperform for the first three turns.

Tyanid Ranged Anti-Tank
Here is the chance each unit has of opening a tin can. I have calculated the probability of dealing with armour in a single shooting phase. I have chosen to display this as a percent since 66% reads much better than 0.66.

First three columns are the chance to Immobilise or Kill AV 14, 13 & 12.
Next two are killing AV 11 & 10. The last column is to the chance to stun AV 12.
Anti-Tank . . . .Immob+ . .Immob+ . Immob+ . Kill . . Kill . . . .Stun+
. . . .VS . . . . .AV14 . . . .AV13 . . . AV12 . . . AV11 . . AV10 . . AV12
3 Zoanthropes . 66.51% . 66.51% . 66.51% . 61.35% . 66.51% . 88.18%
3 Hive Guard .. 10.61% . 36.98% . 56.53% . 50.67% . 61.79% . 91.22%
2 Hive Guard .. 07.20% . 26.50% . 42.61% . 37.57% . 47.34% . 80.25%
T-fex – Rupture 18.50% . 25.85% . 32.85% . 25.85% . 30.56% . 65.97%
HVC . . . . . . . . 02.89% . 05.78% . 08.67% . 05.78% . 7.22% . 26.00%
Harpy TL HVC . . 03.78% . 07.56% . 11.33% . 07.56% . 09.44% . 34.00%
Stranglethorn . . 00.00% . 00.00% . 01.44% . 02.89% . 05.78% . 08.67%
TL Deathspitterx2.0.00% .00.00% . 00.00% . 00.00% . 22.54% . 00.00%
TL Brainleech . . 00.00% . 00.00% . 00.00% . 11.87% . 22.54% . 55.12%
TL Brainleechx2.00.00% . 00.00% . 00.00% . 22.33% . 39.99% . 79.86%
Mycetic Spore . 00.00% . 00.00% . 00.00% . 05.43% . 10.61% . 29.03%
3xLictor FHooks 05.43% . 10.61% . 15.55% . 08.05% . 15.55% . 40.67%
For Comparison -
Marine Lascanx2.14.27% . 24.25% . 33.61% . 27.43% . 33.61% . 69.14%


Carnifex/Trygon Vs Fast Tank (6's to hit)
SK = Screamer-Killer, AG = Adrenal Glands. Claws assumed +2 Attacks
. . . . . . . . . . .Immob/Kill Imm/Kill.Imm/Kill . . Kill . . . Kill . . . Stun+
. . . . . . . . . . .AV14. . . .AV13 . . . AV12 . . AV11 . . . AV10 . . AV12
AG-Trygon . . .. 40.79% . 50.74% . 57.81% . 61.45% . 65.22% . 87.22%
Trygon . . . . . .29.91% . 40.79% . 50.74% . 55.89% . 61.45% . 82.54%
SK-AG-Fex . . .. 50.60% . 53.74% . 55.62% . 56.35% . 56.35% . 83.85%
Skreamer-Killer .46.02% . 50.60% . 53.74% . 55.25% . 56.35% . 82.84%
Dakka-Fex . . . .27.88% . 31.09% . 33.35% . 34.46% . 35.28% . 58.68%
Claw-Fex . . . . 36.72% . 40.62% . 43.33% . 44.65% . 45.61% . 70.99%
Claw/Talon-Fex . 41.54% . 45.77% . 48.69% . 50.09% . 51.13% . 76.93%

Carnifex/Trygon Vs Tank (4+ to hit) Same assumptions as above.
. . . . . . . . . . .Immob/Kill Imm/Kill.Imm/Kill . . Kill . . . Kill . . . Stun+
. . . . . . . . . . .AV14. . . .AV13 . . . AV12 . . AV11 . . . AV10 . . AV12
AG-Trygon .. . 74.44% . 84.82% . 90.42% . 92.74% . 94.76% . 99.90%
Trygon . . . . . 59.63% . 74.44% . 84.82% . 89.04% . 92.74% . 99.58%
SK-AG-Fex . . . 85.77% . 88.46% . 89.92% . 90.46% . 90.46% . 99.90%
Skreamer-Killer.81.28% . 85.77% . 88.46% . 89.64% . 90.46% . 99.85%
Dakka-Fex . . . 65.09% . 70.24% . 73.59% . 75.15% . 76.27% . 96.42%
Claw-Fex . . . .77.09% . 81.68% . 84.50% . 85.76% . 86.65% . 99.05%
Claw/Talon-Fex .82.66% . 86.80% . 89.24% . 90.31% . 91.05% . 99.72%

Charging Monsters
Number of Hits (not Wounds) when Charging WS 4 Infantry.
So here is the math for various Carnifex builds and a Trygon. Keeping a single Talon turned out to give better results than I expected...
Claws assumes +2 Attacks
Carnifex with .. .0 . . . . . .1 . . . . . .2 . . . . . 3 . . . . .4 . . . . . .5 . . . . .6 . . . . .7
Dakkafex . . . . 03.13% . 15.63% . 31.25% . 31.25% . 15.63% . 03.13% . 00.00% . 00.00%
Screamer-Killer 00.10% . 01.46% . 08.79% . 26.37% . 39.55% . 23.73% . 00.00% . 00.00%
Gun/Talon . . . .01.26% . 08.79% . 24.62% . 34.46% . 24.12% . 06.75% . 00.00% . 00.00%
Claws/Gun . . . 00.78% . 05.47% . 16.41% . 27.34% . 27.34% . 16.41% . 05.47% . 00.78%
Claw/Talon . . .00.22% . 02.14% . 08.97% . 20.94% . 29.30% . 24.63% . 11.49% . 02.30%
Trygon . . . . . 00.00% . 00.00% . 00.03% . 00.37% . 03.00% . 14.39% . 38.37% . 43.85%

Screamer-Killer is getting 4+ hits 63.28% of the time.
Claw-fex . . . . is getting 4+ hits 50.00% of the time, 6+ hits 06.25% of the time.
Trygon . . . . . is getting 4+ hits 99.60% of the time, 6+ hits 82.21% of the time.

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