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5Mar/110

Speed Math: The D6 and statistics.

A lot of games that I play use the D6 or standard 6 sided die as a determination of random events (i.e. shooting you in the face).  Ideally a fair die will have a 1/6 chance to roll any result 1-6.  You can use simple knowledges of statistics to determine whether a move is correct or not.

For example: The remnants of a Space marine Tactical Squad consisting of six Space Marines with Bolters and Bolt Pistols is 10" away from a squad of six Chaos Space Marines.  They have three choices.  1: Move up, fire their Bolt Pistols, and assault the Chaos Marines.  2: Remain stationary (or move to a slightly better position less than 12" away) and fire their Bolters twice, or 3: run away!

The tactical situation determines what you should do, but let's use statistics to determine what each choice will entail.

Scenario 1: Because the Space Marine's BS is 4, they hit on a roll of 3+.  This means that, on average, 2/3 of the shots will hit.  This means that the Marines will get 4 hits with their pistols.  These shots wound on a 4+ so 2 of them should wound.  Because the Chaos marines have a 3+ save, the chances that at least one Chaos Marine will die is 1/3 + 2/3 * 1/3, which is a 5/9 chance or about 56%.  Then the Marines charge.  They each get 2 attacks for a total of 12, and hit on a 4+ which means that 6 should hit.  They wound on a 4+ so 3 should wound, and because the Chaos Marines have a 3+ armor save, about 1 Chaos Marine should die.  If a Chaos Marine died from shooting, the Chaos Marines would have 10 attacks, which would generate 5 hits, and 2.5 wounds.  Let's be generous and give them 3.  1 Space Marine would die, and the combat would be a tie.  Next turn, Marines get 5 attacks, Chaos Marines get 8.  Clearly this will end poorly for the Marines.

Scenario 2: The Marines fire 12 times, hit 8 times, and cause 4 wounds, so on average 1 Chaos Marine dies and there's a small chance a second will die.  The Chaos Marines will then move up next turn.  The Chaos Marines are better in assault, so they fire 5 Bolt pistols, Hit 2.5 times which rounds up to 3.  They then wound 1.5 times which we round down (In these scenarios I round up, then down, then up etc.).  Probably not killing a Marine.  They charge getting 15 attacks, 8 hits, and 4 wounds, which will probably kill a Marine but the Marines attack back with 6, hit 3 times, and wound twice, possibly killing a Chaos Marine.  Not as bad, but the Marines are still outclassed by the Chaos Marines and their bolt pistols and close combat weapons.

Scenario 3: Marines move back 6" and run D6" for a total movement of 7-12" away from the Chaos Marines.  If the squad was 10" away, then the Chaos  Marines will be able to shoot the Marines if the final distance is 18" or less.  The Marines more 6" in the movement phase, and are now 16" away.  If the Marines roll a 1 or 2, they will be able to be shot, so this is a 1/3 chance.  The remaining 2/3 chance the Marines will not be able to be shot.

In the end, do you want to pin the Chaos Marines in place?  Harass them and make them advance, essentially baiting them?  Or preserve your squad to hold an objective?  By understanding the math above, you can make an informed decision based on your needs.  Without understanding how well each outcome is likely to be, you may trust in those marines to break the Chaos Marines, which is unlikely.

Once you can do this kind of thing in your head, you can make choices on the battlefield much quicker.

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