Wednesday, 11 April 2012

Ultimate MEq Killer: Mathhammering

What kills a T4, W1 Sv 3+ model? 

Well, anything can, really. 

What? 1 lasgun shot won't kill squat?

Well, be it as it may, The game is dice. 

If something hits on a 4+, wounds on a 5+ and then 3+ cancels it, what does that mean in averages?

Did you know, that that there shot has a 50% chance of hitting?
or that it has a 33.33% chance of wounding?
And only a 66.66% chance of being cancelled out? 

In math, that's a 3/6 chance, a 2/6 chance and a 4/6 chance. 

Overall, that's a 1/6 chance to wound, and a 1/9 chance of actually causing a wound. 

Welcome to math hammer. 
What was the chance of that?
Probabilities: Expressed as fractions. 
Some simple pointers for conversion of /6 into percentages:

6+: 16.67%
5+: 33.33%
4+: 50.00%
3+: 66.66%
2+: 83.33% 
1+: 100.0% 

A model with BS3 shooting a gun with S3 AP- at a target with T4 W1 Sv3+ 

So, BS3 S3 AP- V. T4 W1 Sv3+

There's a:
3/6 chance of hitting
2/6 chance of wounding
4/6 chance of saving

All up, that's a 24/216 chance of fatally wounding, or 1/9. So, for every 9 lasgun shots you should kill one marine. 

A boltgun? BS4 S4 AP5 V T4 W1 Sv3+ 
4/6 chance of hitting 
3/6 chance of wounding
4/6 chance of saving

all up that's 46/216 chance of fatally wounding, almost a 2/9 chance of wounding.

Of a lascannon, plasma rifle or meltagun? 
Since its a 1 wound model and all have an AP better than 3, they're all equally effective! 
Assume: BS4, 2+ to wound V. 1W no save
4/6 chance of hitting 
5/6 chance of wounding
0/6 chance of saving

20/36 chance of wounding (don't count the 0/6 chance, or else it'd be 0/216!) or 5/9 chance of wounding 

1/3 chance of fatally wounding

Never thought of a flamer as an anti-marine weapon, did you? the numbers don't lie.

What about a flamestorm cannon? the weapon specifically built to kill entrenched marines? 
5/6 chance of killing him. 

When you look at all these vaules, you decide on the three best: 

The last three. 

but, you don't stop to consider which of those is actually the most effective. 

the lascannon is likely to kill one marine. but there are, on average, nine more you need to deal with. The plasmagun can get rid of two as well, but there are still 7 more to kill.

Leave it to the boltguns. 

So, one boltgun shot at 12" will kill .33 of a marine. that's 5.28 points! 
You coulda killed .44% of a guardsman instead. and that's only 2.2 points. 

Leaving it to the boltguns, you have at least 17 boltgun shots usually [sergeant may have a bolt pistol, which he does for this example.] 
that's 5.6 marines dead. did you know that? 

That's 89.6 points worth of dead marine. 

The moral of the story: 

Quantity is a quality all of its own: never expect to win anything shooting only the hard hitting weapons. 

In that case, this is my advice:

There's no point getting caught up in having the most high strength, high powered and over powered weaponry if they don't put out enough firepower to stop your enemy. No-one shoots a lascannon at a unit of termagants, though it has almost an 100% chance of killing it in reality. No, you use it on the tervigon behind it, who you have 0% chance of killing outright with one lascannon, but is potentially more of a threat.

When you buy dedicated transports, do you give them lascannons automatically? This is a good thing against mech, you're right, but sometimes 3 S5 AP4 shots would really help you out!

Don't forget your heavy bolters. Don't forget your normal bolters, don't forget to use what you have at your disposal. Use everything to its maximum effect each and every turn, and you stand a far better chance in any game. Don't be afraid to roll 6 lasgun shots, don't be afraid to roll 1 boltgun. it only takes 1 lasgun shot to perform the killing blow on a daemon, however unlikely that may be. You need to think like this and then you will succeed. Don't think in terms of mathammer - think in terms of 'there's a chance' because 'there's a chance' always applies, whereas mathhammer ends when you put the pen and paper down and play a game.

Consider Heavy Bolters. Don't shy away from them. You don't need many, but 4 twin-linked Heavy bolters is potentially 12 dead marines. Don't just go for the biggest and best, remember your staple and don't forget about anti-light infantry and you'll do fine. 
Sometimes, these babies are all you could hope for.