## Monday, March 28, 2011

### Deep Strike Mishaps Risk

How dangerous is deep striking? Well I am going to try to layout a method of estimating the risk of a deep striking mishap. The first step is to figure out the scatter dice probability. RobotBeef over at Mathhammer has a great post on this and I am going to use his method.

Mathhammer

P = ( 1/3 ) + ( ( POSS / 36 ) * 2/3 )
- P=Probability that blast templates won't scatter
- POSS=Number of possibilities 2D6 will be equal to or less than your BS

Using this method we get the following rough percentages for BS 3 and 4 scatter dices:

BS 3 (40-50-70-90 rule)
On Target = 39%
< 2" = 52%
< 4" = 72%
< 6" = 89%
> 6" = 11%

BS 4 (45-60-80-95 rule)
On Target = 44%
< 2" = 61%
< 4" = 81%
< 6" = 94%
> 6" = 6%

We now make a rule that we can remember while playing. For Space Marines it is 45-60-80-95. 45% of the time we will have an On Target result, 60% will be within 2", 80% within 4", 95% within in 6" and 5% greater than 6". You can memorize the number to use as a guide or add it to your quick reference data. Knowing the scatter dice probability helps in targeting templates.

(*Edit for clarity, thanks Farmer Geddon *)

While Deep Strike does not reduce the scatter by the sources BS, the scatter dice probability works the same way. We can use the same math (by using a BS of 0) to work out a rule of thumb. It looks like this:

Deep Strike
On Target = 33%
< 2" = 37%
< 4" = 41%
< 6" = 44%
> 6" = 56%

Here is the Diagram visualize how this pertains to deep strike.

Next let's look work out a rule of thumb for using this information to get a rough estimate of risk. To mishap we need to both scatter the distance the direction of the object we want to avoid. On Target always equal no mishap, so if our On Target percentage is 33% our chance to mishap is lower than 66%. How much lower can be estimated by looking at the chance to land greater than that distance and in that direction.

Anything outside the drift range doesn't affect chance for a mishap nor does anything where you don't drift in the wrong direction. Even on the board edge 33% of the time you will be on target and 50% of the remaining time you will drift away from the edge. That means you risk is only ~33%. If the board edge is 2 inches away 37% of the time you will land On Target or less than 2 inches away from target and 50% of the remaining time you will drift away from the edge. That puts your risk at ~30%. You can start to see where you can do this math in your head once you know the scatter dice probability.

In the below diagram there is a area of terrain we have a mishap risk greater than 2 inches from the target and covering about a quarter of the area.

Right off the bat we know the mishap risk is less than 37% and greater than 0%. In face we can narrow it down more, we know it is 25% of the 41% circle. So we take 59% (100-41%) and divide it in our head 60/4 is 15 so the risk is ~15%. We can lower that risk to ~13% by moving another 2 inches from the terrain.

Using 6th grade math we can estimate the deep strike mishap risk quickly by using the scatter dice probability and simple fractions. Knowing the risk can mean that one inch that wins the game or avoid losing a squad of Terminators.