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# Video Game Logic

## Question

I was playing a mobile video game based on the fall out series.  In this game, you need to arm your citizens with weapons to protect themselves.  When the citizens use the weapons they will hit their target for an amount of damaged indicated within the range given.  Currently, I have a surplus of weapons and would like to allocate the best weapons to my people.  Place the weapons in order of best to worst:

Knife: 0 - 9 damage

Shotgun: 6 damage

Pistol: 5 - 7 damage

Rail gun: 4 - 7 damage

Rifle: 3 - 7 damage

Grenade: 0, 11 (only 2 possible outcomes)

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Depends...

Spoiler

If you go with purely "expected damage value" as your basis for "best", then it would be

1. Shotgun
2. Pistol
4. Rifle
5. Knife

However, I personally would rather have something that guarantees SOME damage over something that has a 50% chance of doing 0 damage (so Railgun > Grenade by that logic). Some people, though, would probably prefer something that CAN do the most damage (Grenade > Railgun)

Either way, the way I see it: the shotgun is the most consistent and highest average damage weapon...so it should be #1. The pistol, railgun, and rifle all do the same MAX damage, but have different min damages...so I would say Pistol, Rail gun, and Rifle in that order...Which gives us:

1. Shotgun
2. Pistol
3. Railgun
4. Rifle

That leaves the Knife and the Grenade and where they should go...while the grenade will do 0 damage 50% of the time, the knife will do the lowest expected value (4.5)...and while the knife CAN do 0 damage some of the time, it won't do 0 damage nearly as often as the grenade. Soooo...if I had to choose, I'd put the Grenade then Knife...so my final order would be:

1. Shotgun
2. Pistol
3. Railgun
4. Rifle
6. Knife

But again, that's my personal preference based on my definition of "best"...and depending on your playing style, risk level, and other unknown factors (does grenade hit multiple targets??), it may vary.

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Another factor to possibly consider...

If enemies have, for example, 7 HP.  The pistol (and the rail gun and even the rifle) would clearly be better than the shotgun.  If they had 6 HP, the shotgun is clearly better than all of them.  If their HP is high enough, these considerations aren't weighted as heavily.

Edited by Molly Mae

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I am not disputing either argument, I am curious though on your thoughts that something like the pistol would be better than the shotgun because

2/3's of the time it is equal or better than the shotgun and only 1/3 of the time is it not.

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Perhaps your question may hinge on the source of variability. Pistol has 5-7. In any skirmish, is the choice between 5, 6, 7 made by the program randomly? Or does it depend upon distance to target? Or visibility ( like heavy, light or no fog)? And, as Pickett points out, damage radius is a key parameter of the Dupuy lethality index.

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