Running the numbers

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varoadstter
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Running the numbers

Post by varoadstter » Mon Jan 28, 2008 9:40 pm

I suppose this already exists somewhere out there but I am working on a bot and have built a simulator class which allows me to run attacks with various numbers of starting and defending armies. Here's what I get when I run the numbers:

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Attacker fixed at 1000 armies each attack
Defender fixed at 1500 armies each attack

Monte Carlo attack simulations
Started at: Mon Jan 28 21:30:06 EST 2008
Ended at: Mon Jan 28 21:30:36 EST 2008
Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 15000000 armies
Attack was successful 0% of the time
Attack failed 100% of the time
Average attacker losses: 999
Average defender losses: 1171
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Attacker fixed at 1000 armies each attack
Defender fixed at 1250 armies each attack

Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 12500000 armies
Attack was successful 8% of the time
Attack failed 92% of the time
Average attacker losses: 997
Average defender losses: 1168
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Attacker fixed at 1000 armies each attack
Defender fixed at 1200 armies each attack

Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 12000000 armies
Attack was successful 30% of the time
Attack failed 70% of the time
Average attacker losses: 989
Average defender losses: 1159
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Attacker fixed at 1000 armies each attack
Defender fixed at 1150 armies each attack

Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 11500000 armies
Attack was successful 63% of the time
Attack failed 37% of the time
Average attacker losses: 969
Average defender losses: 1136
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Attacker fixed at 1000 armies each attack
Defender fixed at 1100 armies each attack

Monte Carlo attack simulations
Started at: Mon Jan 28 21:36:06 EST 2008
Ended at: Mon Jan 28 21:36:34 EST 2008
Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 11000000 armies
Attack was successful 88% of the time
Attack failed 12% of the time
Average attacker losses: 935
Average defender losses: 1097
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Attacker fixed at 1000 armies each attack
Defender fixed at 1050 armies each attack

Monte Carlo attack simulations
Started at: Mon Jan 28 21:37:31 EST 2008
Ended at: Mon Jan 28 21:37:59 EST 2008
Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 10500000 armies
Attack was successful 98% of the time
Attack failed 2% of the time
Average attacker losses: 895
Average defender losses: 1049
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Code: Select all

Attacker fixed at 1000 armies each attack
Defender fixed at 1000 armies each attack

Monte Carlo attack simulations
Started at: Mon Jan 28 21:38:55 EST 2008
Ended at: Mon Jan 28 21:39:22 EST 2008
Ran 10000 simulations
Attacker used a total of 10000000 armies
Defender used a total of 10000000 armies
Attack was successful 99% of the time
Attack failed 1% of the time
Average attacker losses: 852
Average defender losses: 999
----------------------------------------------

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guest
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Post by guest » Mon Jan 28, 2008 11:31 pm

Attack failed 100% of the time

This seems fishy to me. No matter how bad the odds are they aren't zero like this makes it appear. Sure you wouldn't make an attack against a force 1.5 times larger but it should succeed occasionally. Especially since the later tests show the tipping point is around 1000 vs 1175.

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varoadstter
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Post by varoadstter » Tue Jan 29, 2008 12:13 am

guest wrote:Attack failed 100% of the time

This seems fishy to me. No matter how bad the odds are they aren't zero like this makes it appear. Sure you wouldn't make an attack against a force 1.5 times larger but it should succeed occasionally. Especially since the later tests show the tipping point is around 1000 vs 1175.
It may have succeeded somewhat less than 1% of the time. My output is rounding off to the nearest %. I picked a relatively large number of starting armies to alleviate some of the problems with using too small a sample size. If I had used 100 attackers, then even more of the attacks may have failed percentagewise.

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Post by 3DA » Tue Jan 29, 2008 11:05 am

Fascinating. Hey, Varo - remember we were having that discussion about marathons, and how there are strategies to avoid them? These numbers illustrate one of them. There is a point, when the army counts get high enough, that the attacker has a significant advantage. This is the key to ending/winning marathons.

I'd be interested to see the numbers on successful attacks if you took a zero off each starting # of armies: start with 100 for the attacker and 150 for the defender and see what happens. My bet is that the success-failure tipping point moves significantly in favor of the defender.

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varoadstter
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Post by varoadstter » Tue Jan 29, 2008 1:21 pm

3DA wrote:Fascinating. Hey, Varo - remember we were having that discussion about marathons, and how there are strategies to avoid them? These numbers illustrate one of them. There is a point, when the army counts get high enough, that the attacker has a significant advantage. This is the key to ending/winning marathons.

I'd be interested to see the numbers on successful attacks if you took a zero off each starting # of armies: start with 100 for the attacker and 150 for the defender and see what happens. My bet is that the success-failure tipping point moves significantly in favor of the defender.
I'll run it when I get home this evening unless someone else has it handy and can post it (using their own dice simulations).

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