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Author Topic: 2 bears vs. 1 bear Cagematch
sumnchai
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Icon 1 posted August 31, 2005 13:28      Profile for sumnchai     Send New Private Message       Edit/Delete Post   Reply With Quote 
Ok - here's the problem.

In a fight to the death, which would win - one bear with the strength of two bears, or two bears each with the strength of one bear?

Discuss.

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CommanderShroom
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Icon 1 posted August 31, 2005 13:44      Profile for CommanderShroom     Send New Private Message       Edit/Delete Post   Reply With Quote 
I think the tag-team monkey squad would win... [crazy]
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The Famous Druid

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Icon 1 posted August 31, 2005 14:05      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
The double-strength would win.

Bears are quite clever, but they're solitary critters, not a lot of team spirit.

So, 2B would beat the crap out of 1Ba while 1Bb cowered in the corner.
Then 2B beats the crap out of 1Bb.

Now if it was a caged match with wolves.....

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Serenak

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Icon 1 posted August 31, 2005 14:08      Profile for Serenak     Send New Private Message       Edit/Delete Post   Reply With Quote 
On the principle that 5000 ants can bring down an elephant I tend to go with weight of numbers will prevail.

However 2 to 1 is statistically a bit close to call and like most boxing matches I suspect there would be as much luck as judgement in predicting a result.

If I was a betting man I suppose I'd go 5/4 on the two bears - not a lot in it really

[Frown]

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ChildeRoland
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Icon 1 posted August 31, 2005 18:38      Profile for ChildeRoland     Send New Private Message       Edit/Delete Post   Reply With Quote 
I have to agree with TFD. Unless the 2 bears could work together the stronger bear would wipe the floor with them.

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jordanv
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Icon 1 posted August 31, 2005 20:08      Profile for jordanv     Send New Private Message       Edit/Delete Post   Reply With Quote 
I believe game theory could be of some use here.

Variables

Two Strenth Bear : Bear 1

Bears with normal strength : Bear 2A, Bear 2B


Potential Win Scenarios

1) Bear 1 Wins
2) Bear 2 Wins
2a) Bear 2A wins, Bear 2A loses
3a) Bear 2B wins, Bear 2A loses
3) No win situation (they all die)


Assumptions

1) All bears action rational (act in their own best interests)
2) No bear can communicate with another
3) The bears are all aware that victory against the opponent equals survival
4) Their ultimate goal is survival


Strategic Analysis of Rational Choice

Payoff = the utility value to the player, survival being of maximum utility and death equalling a utility value of zero. The possibilities are ranked in this fashion: the higher the value the greater the utility. It is a relative ranking not an absolute ranking so the difference between each option could be great or minor.

Bear 1

Bear 1 is presented with only two choices:

1) Win - payoff 1 (survive)
2) Lose - payoff 0 (die)


Bear 2A

1) Survive, minor win (2B dies) payoff 4
2) Survive, total win (2B also survives) payoff 3
3) Loss - both bears die - payoff 2
4) Loss - the bear dies - payoff 1

Bear 2B

swap 2A with 2B in all instances in the previous section.


Now, the optimal result for Bears 2A and 2B would be a total win. Going back to the assumption, however, that the ultimate aim of the bears is survival then the rational action of each of 2A and 2B would be to increase the chance of survival. In this situation, the outcome with the highest utility would be a minor win as this minimises harm. This involves waiting for the other partner in the alliance to strike first..

Prisoner's dilemma?

Now I think this can be regarded as a form of prisoner's dilemma because the rational choice of bear's 2A and 2B would be to not attack first. If both bears act rationally, then neither will attack first or cooperate with the other which means both will lose.

Obviously this is not the optimal result, as they need their combined strength to defeat the bear (all other things being equal). Indeed I don't think the optimal result (Bears 2A & B) can ever arise as both have an incentive to cheat (minimising harm) without a threat of punishment.

Conclusion

Bear 1 will totally kick the arses of Bears 2A and 2B because they will be acting rationally and not co-operate.

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csk

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Icon 1 posted August 31, 2005 20:42      Profile for csk     Send New Private Message       Edit/Delete Post   Reply With Quote 
Nice analysis jordanv [thumbsup]

So, interesting spanner into the mix. Do the two weaker bears know beforehand that the other bear is twice as strong? Does it make a difference to the outcome?

Of course, another weaker bear strategy is to basically attack the stronger bear in the back while he's attacking the other weaker bear. Of course, the weaker bear is only likely to use this strategy if he realises he can't beat the stronger one on his own.

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The Famous Druid

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Icon 1 posted August 31, 2005 21:20      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Jordans analysis is interesting, but the payoff numbers are debatable.

What are the LittleBears motivations?

Are they there to kill BigBear at any cost?
If so, the death of BigBear can be considered a 'win' even if achieved at the cost of ones own life.

Or are they simply trying to survive?
If that's the case awarding different payoffs for 'both LittleBears survive' and 'other LittleBear is killed but I survive' is debatable, and depends on the LittleBears attitudes to each other. Are they brothers? Mother and child? Total strangers?

And did they take a sh1t in the woods first?

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csk

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Icon 1 posted August 31, 2005 22:59      Profile for csk     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
Or are they simply trying to survive?
If that's the case awarding different payoffs for 'both LittleBears survive' and 'other LittleBear is killed but I survive' is debatable, and depends on the LittleBears attitudes to each other. Are they brothers? Mother and child? Total strangers?

Of course, we could complicate it further. What happens if the cage matches are simply repeated with equivalent replacement bears ad-infinitum. Does the winning payoff for an individual bear decline over time versus the losing one?

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jordanv
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Icon 1 posted August 31, 2005 23:10      Profile for jordanv     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
Jordans analysis is interesting, but the payoff numbers are debatable.

What are the LittleBears motivations?

Are they there to kill BigBear at any cost?
If so, the death of BigBear can be considered a 'win' even if achieved at the cost of ones own life.

My assumptions were that the teamed bears understood that if they killed their opponent they would survive. So fundamentally their main motivation was survival.

Hmm I assumed they didn't know the other bear was twice as strong, but knew it presented a threat to them (ie 2A and 2B knew 1 was at least as powerful as each of them respectively)

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The Famous Druid

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Icon 1 posted August 31, 2005 23:52      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by jordanv:
My assumptions were that the teamed bears understood that if they killed their opponent they would survive. So fundamentally their main motivation was survival.

Ah, but having finished off BigBear, would they then be expected to fight each other?

That would alter things quite a bit.

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NOP
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Icon 1 posted September 01, 2005 01:26      Profile for NOP     Send New Private Message       Edit/Delete Post   Reply With Quote 
I think the answer to this would come through experimentation. Does anyone have any spare bears and a cage?
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jordanv
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Icon 1 posted September 01, 2005 02:08      Profile for jordanv     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
Ah, but having finished off BigBear, would they then be expected to fight each other?

That would alter things quite a bit.

Yeah, the original question was very ambiguous on that.

Also, the experimentation idea is a good thing. To avoid PETA though, we shall use humans.

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NOP
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Icon 1 posted September 01, 2005 04:30      Profile for NOP     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by jordanv:
Also, the experimentation idea is a good thing. To avoid PETA though, we shall use humans.

Does anyone have any spare animal rights actavists and a cage, then [evil] ?
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Stereo

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Icon 12 posted September 01, 2005 07:03      Profile for Stereo     Send New Private Message       Edit/Delete Post   Reply With Quote 
Jordanv, I do agree the analysis is fine, but if you allow me to nitpick, you should edit your analysis post to straighten up your identifiers. You first define bear B1 and B2, then immediately after call them 2A and 2B. Also, it would be nice to maintain the situations in the order originally presented: 1, 2, 2a, 2b, 3.

Ok, I know you didn't mean to write a math book, but even when coding, changing the variable's names along the code is bad. (That's why I always force variable declaration - if possible - in languages with automatic declaration.)

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alfrin
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Icon 1 posted September 01, 2005 08:26      Profile for alfrin     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by NOP:
I think the answer to this would come through experimentation. Does anyone have any spare bears and a cage?

Oh yeh, I keep a fresh supply in my pantry for just the occasion

I think it is argueable the BigBear probably has twice the brain of the LittleBears, thinking of that , couldn't the BigBear play mind games with the "Not -So-Smart" LittleBears and pit them against themselves, the littlebears will fight each other, leaving only one little bear for the big bear to fight. Then we have the usual Bigger 1 versus Smaller . Giving the BigBear absolute victory

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sumnchai
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Icon 1 posted September 01, 2005 09:54      Profile for sumnchai     Send New Private Message       Edit/Delete Post   Reply With Quote 
To clarify a few points on my original question.

A cagematch. They are fighting to the death.

The two bears each with the strength on one bear are allied and on the same side.

What happens after the battle is immaterial - take it as an isolated event.

I say the one bear with strength of two bears will win. (For the same reason as the 5000 ants and one elephant.)

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Sxeptomaniac

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Icon 1 posted September 01, 2005 09:54      Profile for Sxeptomaniac   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Anyone else reminded of bearbaiting? Thank goodness that's been illegal for a long time.

Well, here's my take on this odd hypothetical situation, putting aside motivation and such:

Even for Bigbear, claws and blows would probably not be enough to finish the Littlebears. He would have to bite, which would expose his throat to the other Littlebear. Once either of the Littlebears were to latch their jaws onto the Bigbear's throat, it would probably be the end of the match.

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jordanv
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Icon 1 posted September 01, 2005 16:47      Profile for jordanv     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Stereo:
Ok, I know you didn't mean to write a math book, but even when coding, changing the variable's names along the code is bad. (That's why I always force variable declaration - if possible - in languages with automatic declaration.)

Gimme a break I was drunk at the time ^_^.

I'll do the editing now to fix up the post though.

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