American soldier awaiting German counterattack (Photo credit: Za Rodinu)

I still remember my Grade 9 math classes on Probability. Those classes are perhaps one of the most useful ones I ever had. My teacher took all the most common casino games and lotteries schemes and had us calculate the probabilities of different outcomes for each. You can imagine how delightfully interesting that semester was.

One result is that I don’t gamble all my adult life because we proved to ourselves mathematically that the house ALWAYS win.

Probability plays a huge part in Advanced Squad Leader through the use of dice rolls (“DR”). As with life, different decisions carry different levels of risk and are reflected through the use of dice rolls in the ASL world. Grognards I play with have probability tables committed to memory.

So what does this all translate to?

A Light Machine Gun (“LMG”) rate of fire is “1”.  That means LMGs have a 16.67% chance of firing again and a 2.78% chance of firing 3 times. For Heavy Machine Guns (“HMG”) with their rate of fire of “3”, their chances of being able to fire again goes to 50%. There’s a 25% chance of the HMG being to fire the third time.  If you take into the account that HMGs malfunction at a DR of 12, the probability of HMGs being able to fire a third time without malfunctioning is 22.97%.

Think of that the next time your squad face one down.

Sniper rules in ASL are interesting. For some, it stops us from firing off every squad on the board when the odds of shots having any effect is low. However, the probability of a DR triggering a SAN and for the sniper to active is actually pretty low. A SAN of 4 gets triggered only 3 out of 36 possible outcomes with two dice. You need a further roll of 1 or 2 on a single die for that sniper to be active.  End result? A SAN of 4  triggers a sniper with some effect only 2.78% of the time.

I read Mr. Robert Medrow’s excellent article “First Impressions – A Introduction to Advanced Squad Leader : Infantry Training” almost a year ago when I first looked to learn the game. It didn’t hit me much at the time. A big stack of games afterwards, it certainly does. It’s in Avalon Hill The General Magazine, Vol 22 Number 6.

Take a look at Mr. Medrow’s Table 5 “Probability that a single unit will survive and attack either unharmed and unpinned or (unharmed and pinned)”. One of the games I am currently playing has SS troopers (Morale level 8) attacking 1st Line Russian squads (Firepower 4). That means if a SS squad run across the open, its chances of survival is 49% (Table c). Those opportunities are hard to come by however, if the squad decides to Assault Move on open ground, its chances of survival is 60%.  If I can’t hit it while on the move but try to shoot at it during my Prep Fire, its chances rise to a whopping 94% sitting in some stone buildings!  However while I have 6% chance of doing anything to it, I have only 0.93% chance of being sniper bait (German SAN 2). I might just go head and take the shot anyway, for lack of better alternatives.

On the contrary, my Russian squads are fine 91% of the time sitting in stone buildings against inherent firepower from the SS squads.  They have a 84% chance against an HMG firing once but a 70.6% against HMG being able to fire twice, which is 50% of the time.  Against HMG firing 3 times (25% probability), their survival dropped to 59.3%.  That is lower odds than squads getting caught in the line of fire while skulking – 64% against inherent firepower.

See how much fun it is? Plus that’s just with one of Mr. Medrow’s probability tables. Every action in ASL carries with it the inherent benefits and risk. It’s the optimisation of these choices that makes Advanced Squad Leader so perpetually engaging!

Resources :

• “Basic Probability Primer for ASL” by von Marwitz