Return on investment on Garrison armies.

[IkkeTM]

When I started playing risk I got the advice to always leave behind two armies on a country as garrison.

So I decided to do the math on how dearly a garrison in a country sells their hide when they get overrun by insurmountable odds.

Calculations:

Spoiler

Using http://gamesbyemail.com/games/gambit/battleodds to calculate the odds of killing a certain amount of troops, multiplying that with the number of kills to get the expected payout value, cutoff being at odds below 0.01% - rounding up to compensate for cutoff:

1 Army:
22.44888+7.63886*2+2.59933*3+0.88450*4+0.30097*5+0.10241*6+0.03485*7+0.01186*8 = 51.52073 = 0.52

2 Armies:
22.15194*1+18.41125*2+9.04587*3+6.25932*4+2.94352*5+1.93233*6+0.89556*7+0.57704*8+0.26599*9+0.17018*10+0.07828*11+0.04994*12+0.02296*13+0.01463*14 = 154.40552 = 1.55

3 Armies:
20.82263*1+17.45058*2+13.24014*3+8.47158*4+6.08722*5+3.50493*6+2.44270*7+1.33054*8+0.90991*9+0.47910*10+0.32352*11+0.16651*12+0.11144*13+0.05643*14+0.03752*15+0.01877*16+0.01242*17 = 230.38946

4 Armies:

16.46582*1+17.87559*2+14.03881*3+12.00185*4+8.04583*5+6.27345*6+3.86366*7+2.87007*8+1.67600*9+1.20846*10+0.68031*11+0.48075*12+0.26348*13+0.18351*14+0.09853*15+0.06788*16+0.03586*17+0.02449*18+0.01277*19 = 320.25949

Results:

1 Army : 0.52 killed / defending army
2 Armies: 0.77 killed / defending army
3 Armies: 0.77 killed / defending army
4 Armies: 0.80 killed / defending army

Conclusion seems to be that leaving behind 2 armies is about 150% more effective than leaving behind 1 army. After that, addition armies have very little effect until you start to reach equivalent numbers to the attacking armies.

Ideal defensive set up then, would be to have one stack which is as large as possible, leaving 2 armies to occupy the lands behind.

Given that it trades at a loss, this brings us to the next question: Under what conditions is it profitable to take an army from the garrison and contribute it to an attack? (in maps with less restrained reinforcement rules) Maybe next time.

[jleonnn]

not too sure if i understood what you were saying but I think generally leaving a 2 on your territories is almost always the safer option on the average map, particularly the smaller ones because the additional +1 troop deploy per 3 territories is very valuable. Plus, unless the number of troops your opponent has is really big, chances are any attack he launches on you will fizzle out if you have a bunch of territories with 2's on them then you can launch your own cautious counterattack. I guess the only exception to this would be if you need troops to prevent your opponent from taking a bonus that would seal his victory. Or if you're playing on trench settings

[Silly Knig-it]

Two exceptions to this that I can think of quickly. But I agree with you overall.

1. Playing trench, since I know you can only take one tert from me, I find having the extra ones, that would be in garrison more useful up with the forward troops. (And yes you could be touching 4 terts and thus take four from me, which doesn't change the big picture answer. Yes tactics and strategy are different.) And the more terts I have the bigger the effect. (i.e. if I have 10 terts, that would be an additional 10 in garrison that are not up where I can use them.

2. In an assassin game, not having the extras up where I can use them could be the difference between a win and a loss.

Again, thanks for the stats.

[iancanton]

when defending, the figures above show that 2 troops is much better than 1.

however, in 1v1 games, u need to use a more aggressive formation, not only because ur troops kill more enemy troops when attacking than when defending, but also because region count plays a bigger part at the beginning.

ian.

[niMic]

2 is good defensively, of course, but many people overdo it. Particularly in team games, it's often more benefitial to use them as attacking dice than having them sit there as defensive dice. I don't play much (or any) 1v1, so I can't tell you about that.

[Razorvich]

Then there is the dice.

1 man is an easy beat..... 2 men + MOJO, can take out an army