The hatred these two have for each other is palpable in the "Overheard at the Paizo office" thread.
Who will win, and who should be fired?
Let's fight it out mad max style.
The hatred these two have for each other is palpable in
the "Overheard at the Paizo office" thread.Who will win, and who should be fired?
Let's fight it out mad max style.
Pssshaw. Cosmo's 'stache could take Byers.
Pssshaw. Cosmo's 'stache could take Byers.The hatred these two have for each other is palpable in
the "Overheard at the Paizo office" thread.Who will win, and who should be fired?
Let's fight it out mad max style.
Indeed.
Malaise-Inducement Construct
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Let's fight it out mad max style.
Heh... It's always so silly when Ross hops on Bulmahn's back and they try to take me on, Master Blaster-style. They're so cute when they think they're getting all scary like that.
Wait? What? Ross can actually jump that high?
Ross vs. Cosmo.
I seen it.
Mostly in traffic on 520.
It ain't purdy.
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Let's fight it out mad max style.
Heh... It's always so silly when Ross hops on Bulmahn's back and they try to take me on, Master Blaster-style. They're so cute when they think they're getting all scary like that.
How have I missed that avatar until now? I love it.
How have I missed that avatar until now? I love it.
I've been told that he's kept in reserve for only the specialest of postings.
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The hatred these two have for each other is palpable in the "Overheard at the Paizo office" thread.
Who will win, and who should be fired?
Let's fight it out mad max style.
Doesn't Cosmo have a fear aura?
Does Ross have facial hair? 'Cause, if he does, he & Cosmo can settle this the modern way... on TV!
Does Ross have facial hair? 'Cause, if he does, he & Cosmo can settle this the modern way... on TV!
I don't.
Also, this'd be a short fight. Cosmo carries a box cutter.
what, he doesn't use a machette? That's kind of... disapointing.
what, he doesn't use a machete? That's kind of... disappointing.
Cosmo is still a padawan learner. He doesn't get a machete until Master Trejo feels has enough experience with the Force.
A simple dueling game:
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Consider a duel between two players, Ross and Cosmo. Each has a nerf
pistol with only one shot.
They start far away from each other, and begin to slowly advance. As they get closer the
chance of hitting goes up. But each does not want to wait too long (get too close)
because the other's chance of hitting is increasing all the time.
Lets model this and say, Ross and Cosmo start the duel at a distance t = 1 from each other.
They approach each other at the same speed, and each has to decide when to shoot.
As they get closer to each other, their accuracy increases. At distance t, Ross has a
chance a(t) of killing his opponent, and for Cosmo it is b(t). Assume both players are
aware of the other’s skill.
In this duel, missing your shot is very costly. If a Ross shoots and misses, then Cosmo
keeps approaching until he gets to point blank range and shoots with complete accuracy.
What is the optimal strategy of this game? That is, at what point should each player shoot?
The tricky part to the game is balancing when to shoot. If you fire too early, then your opponent
kills you for sure. If you wait too long, then you can also get beaten if your opponent is
a good shot.
We can think about when Ross should fire by listing out the chance of surviving in the
different possibilities of firing at point t.
Now we can reason out Ross‘s strategy. Ross will want to fire first if his chance of hitting
is greater than Cosmo‘s chance of missing:
a(t) ≥ 1 – b(t)
But he must also be careful not to fire too early. He should always wait if his chance of
hitting is smaller than Cosmo’s chance of missing:
a(t) ≤ 1 – b(t)
Putting those two equations together, we can see that Ross should shoot at the time when he is
at distance t* where
a(t*) = 1 – b(t*)
Or alternately written,
a(t*) + b(t*) = 1
We can do the same exercise for Cosmo. Notice the same conditions are true:
Now we can reason out Cosmo‘s strategy. Cosmo will fire first, if his chance of hitting is
better than his opponent’s chance of missing:
b(t) ≥ 1 – a(t)
But he must also be sure not to fire too soon. He needs to wait so long as his chance of hitting
is smaller than his opponent’s chance of missing:
b(t) ≤ 1 – a(t)
Putting those two equations together, we can see that Cosmo should shoot at the time when
he is distance t* where
b(t*) = 1 – a(t*)
Or alternately written,
a(t*) + b(t*) = 1
From the equations, you’ll notice that both Ross and Cosmo choose to fire at the same time!
There is one specific distance which is optimal for both players.
This would not be surprising if these two had the same accuracy level. But we solved this game
using the assumption their accuracy levels were different.
So why do they end up shooting at the same time?
We can reason why this must be the case. If one person chose to fire earlier than another,
say 5 seconds earlier, then he would be better off waiting. His opponent is not shooting
for another 5 seconds, so he might as well wait a few more seconds to get closer and increase
his accuracy.
As the equations show above, the right time to shoot is just when your chance of hitting equals
your opponents chance of missing. And since one person’s failure is another person’s success,
this means both players choose the same time when they are a distance such that their accuracy
functions sum to a probability of 1.
Director of Sales
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Well, did Cosmo finally win?
:)
what, he doesn't use a machette? That's kind of... disappointing.
The shorter the knife, the closer one needs to be to get the kill. The closer one needs to be, more skillful one needs to be to get the kill.
A box knife only has a 3/4" blade.
Maybe they can duel with Rock, Paper, Scissors.
S,P,R,R,S,P,P,R,S
S,S,S,P,P,R,S,S,R,P
Both of your strategies were both foiled in one try by my wife. Just FYI.Maybe they can duel with Rock, Paper, Scissors.
** spoiler omitted **
** spoiler omitted **
Try this one: S,P,P,S,P,P,S,S,R,R