Calculating averages

4th Edition

My thanks to Follow for allowing me to reproduce this article.

We all know dice are important to the game. We all know that rolling high is what we want and a 3+ means it's easier to do than a 4+. But how important is it to know exactly what your odds are?

The answer of course is very important, or I wouldn't write all this stuff about it would I? Sardonic hall of fame here I come! In all seriousness, knowing the odds of certain actions and even the odds of certain death is the difference between a carefully calculated assault, and a blind flight into the maw of death!

1. Blowing stuff up with guns!

Lascannons do this pretty well, as do Demolishers, and anything else with Str9 or so. But how well exactly? As difficult as it may seem, it's really not such an overwhelming task to look into the numbers, and usually to figure this stuff out doesn't even require a calculator. I can cover a few tables here but there is no way to make one on every single scenario possible. If you do make one of those though, please me know, I for one would print it out and use it

Example 1: Lascannon vs. Land Raider!

In the hands of a Space Marine, you will hit with your lascannon approximately 66% of the time (2/3), got it! Now when it hits, you're looking at a 16.5% (1/6) chance that you will inflict a glancing hit, a 16.5% (1/6) chance of a penetrating hit, and a 66% (2/3) chance that you will do nothing. Again, easy enough to state, but when you're looking into averages you need to also take into account the possibility of these numbers coming up together! This is the oversight most errors come from and statistically 90% of mistaken averages I look at are because of this seemingly simple mistake (man, it just kills me sometimes).

So how do we figure out this elusive togetherness of numbers? Well, I can point you to various websites on how to do it where some pencil neck will speak over your head and thoroughly confuse you or I can give you the simple format. I'm a nice guy like that, so here it is:

In the Land Raider example above, we have a 66% chance of hitting the tank itself. So now we take this figure and check what 16.5% of it is, easy enough 66 x .165 = 10.89% chance of either a glancing or penetrating hit from start to finish, or 21.78% (calculated by simply adding 10.89 and 10.89) of any type of damage whatsoever from start to finish. That means there is a 1-in-5 chance that lascannons will do any kind of damage to your vehicle and 1-in-10 will cause a penetrating hit. We can also break this down farther to see that there is a 5.445% chance that the Land Raider will be destroyed by a penetrating hit, and a 1.79685% chance that it will be blown up AND have a d6 inch explosion (that's about 1 in 50 times)! Just keep taking your numbers and check your percentages.

The only basics you need to know is that there is a 16.5% (1/6), rounding down to nearest half decimal, chance of any pip landing on a die at any time you roll, and the percentage multiplied by the percentage is your chance of getting them both together!

2. Assaulting stuff

Assaults add another aspect to your karmic dice gamble. You not only have the consideration of your rolls and how likely you are to kill your opponent, but you have to also worry about armour saves, attacks back, initiative, charges, etc. Overwhelming? Not really, it's just another way of doing the same number; you might have to multiply a few more things though.

Example 2: Space Marines v Howling Banshees

Let's make our example 5 Assault Marines against 5 Howling Banshees. The most immediate difference is that we're going to want to look at not the possibility of death among the marines, but how many will die in the initial assault. We can assume the Banshees got the charge.

15 attacks that will hit 50% of the time means 7.5 hits among them. Of these, 33% of them will kill a marine. That means, we're looking at 2 dead marines and a possibility of a third before they even get to strike back.

Let's assume only 2 died this round and have our intrepid marines make their attack back. We have 3 marines making 2 attacks each for a total of 6, of which 3 (50%) will land. Now the marines have a 66% chance of wounding the Banshee (Str4 vs. T3), so 2 wounds. The Banshees have a 4+ save which is 50%, so one dead Banshee.

Next round begins; it's the marine's turn. 4 Banshees attack with 8 attacks 4 of which will hit, and 1.32 (33% of 4 hits) will wound. This is under the .50 mark so we will say one more marine corpse. Now we have 2 marines left who make 4 attacks in return, of which 2 hit and 1.32 wound. One more Banshee corpse is added to the pile, three left!

Next round heralds 6 attacks from the Banshees, 3 hits, and 1 wound (basically you're looking at 1 wound per 6 attacks from them). Only one marine left against three Banshees! He strikes back, 1 hit, and 1 wound. It's unlikely that he will kill one this round. In fact, the odds are only 33% that he will kill one as follows: 2 attacks at 50% chance to hit, so 1 will hit. 66% chance of a wound, and 50% chance that the Banshee player will save it, which decreases the 66% chance to 33% (66 x .5 = 33). So our marine will probably die in the Eldar player's turn after 2 rounds of valiant combat.

So why is all of this important? I'm sure we all saw this coming, right? We knew that charging Banshees are meant to kill stupid marines, DUH! Knowing the numbers like we do will give us a few advantages, first and foremost, we can see from the numbers above how many in a squad we are likely to have after our assault. Furthermore, we can also estimate the amount of time it will take in rounds to accomplish your goal and if it's worthwhile to you. Also, you can estimate the amount of time you'll be able to tie your opponent's unit up so that the rest of your army is able to do something else. There is no such thing as knowledge that isn't valuable in some way!

3. The Dice Gods hate me!

Yes, they do. I've told you before and I'll say it again, they've told me that they hate you. Such is life. In fact, humans are naturally fatalistic and will see the most horrible outcomes and remember them rather than the glorious successes. I assure you that if you took a single 6-sided die, and rolled it a million times, you will have approximately 500k results 1-3, and another 500k 4-6, that's just how things work. The deviation you will see will be negligible at best. So it stands to reason that out of the million rolls you've made playing 40K, your deviation is also negligible. That's just how science works! But, when throwing one dice at any single point.

4. Conclusion

Dice rolls will not win or lose your games consistently, that is left to your strategy and brilliance on the field. Your best bet is to exploit your opponents' weaknesses with your strengths and rely on the averages to see you through it more times than not. When you can calculate (or at least estimate) all of these numbers immediately on the field, you can tell where your units will be most effective and how to render your opponent least effective. That is the key to a winning strategy.

May the dice gods be with you
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