Throughout this Strategy and Tactic’s blog, you’ll see me referencing numbers, percentages, and probabilities. Sitting down typing, I’ll be a lot more tempted to work out the exact probabilities of what you want (or what you don’t want) occurring, and I might even get into some more complex stuff too (like saying “you can be 95% confident that you’ll score between 3 and 5 hits).
However, for most of us involved in the fast-paced games where stuff actually happens, or those of us playing a tournament, you're not going to have the luxury of time and paper or a graphing calculator.
So much of the time I see people discussing probabilities online. They say that a certain event is so exactly probable. Like, a bolter shot fired from a Space Marine Tactical Squad has a 66.6% chance of hitting. If the Marine fires 2 shots, he has a 50% chance that both hit and a 75% chance that at least 1 hit. Etc., etc.
This ISN’T helpful for the majority of people, mostly because it’s too in-depth. A lot of people just want to know if what they want to happen has a favourable chance of happening, or not. Heck, most people don’t even know what a favourable chance is.
So, I’m going to give you a quick and dirty run-down of how to judge your chances on the fly. This method should help you size up your chances within 10 seconds. If it takes longer than this, then you probably don’t have a favourable chance, or you’re dealing with a very complex situation.
Effectively, to do this you are going to break the rules of standard probability calculations. You’re going to wind up with numbers over 100%, which normally is not allowed, you’re going to add when you should multiply, and you’re going to estimate when you should calculate.
Step 1: Know the Odds
Memorize this.
6+ = 16% or 1/6
5+ = 33% or 1/3
4+ = 50% or 1/2
3+ = 66% or 2/3
2+ = 83% or 5/6
1+ = you never have a 1+, but it’s 100%
It’s imperative that you know these numbers or fractions. I put down both, because I like working with fractions (seriously, when you understand fractions and can do them in your head, all of math becomes easier to handle).
Step 2: Add
Any time that you have a chance of doing something, add these together. If I fire two bolter shots from a Space Marine Tactical Squad, I have a 130% chance of hitting with at least one. Or, in other words, often 1 hits, sometimes 2 hit, but rarely will none hit. Why? Well, 100% means that you have a good chance of it happening. It’s not perfect (perfect does not exist in this system) 100% merely means a good chance that at least 1 of what you are trying to determine will happen. 30% means that sometimes, though not often, 1 MORE will hit. Now, you know that there’s a chance that neither shot will hit, but that’s a different chance calculation (specifically, 33% + 33% = 66%, is less than 100%, so not a good chance, but it’s there).
When dealing with larger shots, knowing fractions will help. Say it’s 24 shots. Well, 24 * (2/3) will give you 48/3. Don’t worry if you can’t do that division, you can guess that 3 goes into 48 at least 12 times. That’s quite a bit lower than in reality, but you don’t need to know that it’s exactly 16 times (besides, exact figures are misleading). 12 is a figure you can count on – meaning that you should be able to hit 12 times. You may get more, but it’s unlikely that you’ll get less since you under-estimated.
If you do shoot for exact estimations (like 16 in this case), you will find that 50% of the time you score this or more, and 50% of the time you’ll score this or less. This isn’t a probability study, this is a tactical survey.
Step 3: Determine Best Decision
So you know that you should hit more than 12 times. Will that be enough? At this point you should be able to know (shooting at Gaunts, you’ll kill a good number of them, 7 or 8 probably, shooting at Space Marines, you’ll get maybe 1 or 2… maybe none at all). If not, continue you’re fast calculations.
Guants: 12 * (2/3) = 24/3 = 8, no saves, 8 dead
Space Marines: 12 * (1/2) * (1/3) = 12/2 * (1/3) = 6 * (1/3) = 6/3 = 2 dead
What will this accomplish? Will the Gaunts be neutered? Will the Space Marines be forced to make a Ld test? Will this even the odds in Assault? That tactical decision will still be up to you, but you are now armed with info that can be compared to other information and your strategy in order to determine the best choice.
Remember, however, that this system is for BASICS only. Things get MUCH more complicated than this, but your understanding of this basic concept is rather critical. You need to know this math in order to make statistically good decisions. Just remember, for best comparisons, guess on the low side. This game involves a strong element of chance. Sometimes, even a statistically favourable event will go catastrophically wrong.
For example, one time I had a squad of genestealers assault a Land Raider back when Rending gave you an extra D6 (not an extra D3). By all probability, the Land Raider should have been toast – but it didn’t, and its hurricane bolters then proceeded to munch apart my Genestealers – a devastating blow to my army (I was already getting low on units that could deal death-blows to my enemy).
A Note on Unfavourable Situations:
Sometimes an event is unfavourable, but you should take it anyways. A great example of this is when shooting at tanks. Technically speaking, a single Lascannon has a poor chance of killing any vehicle, simply because over half of the Vehicle Damage table gives a result that is NOT destroyed. Even the dreaded Tau Railgun has a less than 50% chance of destroying even an Armour 10 vehicle (1/2 to hit, 1/2 to destroy… remember that being AP1 gives it +1 to its damage roll = 1/4, or 25%... and we’re not even counting the vehicle as hull-down for an additional 1/2 chance that it shrugs off the hit).
However, it still makes sense to include these in your army because, when it DOES destroy a tank, it will often deal a very large blow to the enemy. Tactically speaking, it has the best chance-to-impact ratio out of your whole army by targeting the enemy’s vehicles. Impact is the tactical blow that losing that unit will cause to your opponent. It cannot be directly measured (destroying that Demolisher in range of your Terminators is a much greater blow than destroying that Demolisher that’s 48” away from anything).
Determining that ratio will largely be determined by you, as a tactical decision governed by your strategy.
No comments:
Post a Comment