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  #1  
Old October 9th, 2007, 08:50 PM
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Rolling the D20

First, I want to start this thread by officially stating that this is not an attempt to start trouble. This topic was beat nearly to death a few months ago in another thread, and eventually it was dropped. However, I am still not convinced that my reasoning is incorrect. With this new thread, my hope is to get to the bottom of this issue once and for all. Not to prove whether I'm right or wrong, but because it affects how I play the game. That said, let the fun begin:

The original debate started over the use of Grimnak's Chomp ability. The card states that you must roll a 16 or higher to use the ability on a unique hero. On a 20-sided die, the numbers 16-20 (5 numbers) represent a 5/20 chance of a successful Chomp. This translates to 1/4 or 25%. This part can be considered fact, as no one was debating this point. What follows is my stance on the issue.

Browncoat's Theory
I maintain that no matter how many times the D20 is rolled, the success rate for Chomp (or any other D20) roll remains the same. Meaning, that on the first roll, you have a 25% chance. On the second roll, a 25% chance. On the 4,376th roll...25%.

I back my theory with some mathematical facts known as Gambler's Fallacy, the Law of Large Numbers, and the Law of Averages. You can look these up at your leisure, from whatever source you choose. In summary:

Gambler's Fallacy: It is the incorrect belief that the likelihood of a random event can be affected by or predicted from other, independent events.

An example of Gambler's Fallacy is a coin toss. You have a 50% chance of the coin being heads. The chance of heads coming up twice in a row is 25% (0.50.5=0.25). If the coin was tossed and heads came up 4 times in a row, a believer of this fallacy would state that heads coming up on the 5th toss would have a 1/32 chance. This is incorrect.

The probability of getting heads has not changed at 50% (1/2). While a run of 5 heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they do not count. This holds true to the rolling of the D20 for the Chomp ability.

In summary: Prior failure (to get 16-20) and the need for additional rolls, does not increase the odds of future success. Each roll is a completely independent action, and the odds of 25% remains constant. The only way to increase the odds is to somehow physically remove the side of the die of an undesired result. For example, if a 3 is rolled, that side of the die is removed, in effect making it a D19 for the next roll...thus increasing the odds.

The Other Theory
In the previous thread, I was the lone subscriber to the above theory. What is posted below is what was largely being debated against me:

Quote:
To explain the chomp numbers: each chomp has a 25% chance of success, but only one needs to succeed. In one attempt, you have a 25% chance of getting that one success. If, and only if, that attempt fails you will then have a 25% chance of success on a second attempt. At this point, you have the original 25% plus another 25% of the 75% chance that the first attempt did not succeed, for a total of 43.75% chance of having succeed once after two attempts. Should the second attempt also fail, a third attempt adds another 25% of the 56.25% chance that you failed on both of the first two attempts; this brings you to 57.8125% chance of having gotten a single success after three attempts.
Quote:
The odds of Grimnack Chomping on 1 try is 5/20=25%
The odds of Grimnak NOT Chomoping on 3 tries is 3/4 x 3/4x 3/4=27/64

Therefore if he has a 27/64 probability of not chomping then he has a 37/64 chance of a SUCCESSFUL Chomp
I have quoted replies from the original thread because honestly, I don't understand their logic enough to duplicate it here in my own words.

Disclaimer
Again, I wish to stress the fact that I do not wish to turn this into a heated debate a la Homba style, especially in light of recent events. If I am incorrect, perhaps it's my inability to understand the above quotes. Obviously I feel my own theory is the correct one, but would very much appreciate more feedback on this topic. Thank you!
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  #2  
Old October 9th, 2007, 08:53 PM
Avenger Avenger is offline
 
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I don't really undesratnd what you guys were debating, but the only reason the percentages would decrease over multiple rolls is if you're trying to get multiple successful roles all in a role. Does that make sense?
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Old October 9th, 2007, 09:00 PM
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You're both correct. Why was there an argument?
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Old October 9th, 2007, 09:01 PM
Avenger Avenger is offline
 
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I don't know. Browncoat?
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Old October 9th, 2007, 09:03 PM
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Quote:
Originally Posted by Mooseman
You're both correct. Why was there an argument?
I'm also curious.
How can you beat math?
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Old October 9th, 2007, 09:07 PM
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Browncoat Browncoat is offline
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In response:

The original thread was a 200 point army thread. I suggested an army of Kaemon Awa and Raelin, which is 200 points. I was lamented because it was only a 2 figure army...which led to the argument about Grimnak being able to Chomp my figures with ease. To which I made my stance on the 25% success rate.
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Old October 9th, 2007, 09:15 PM
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I say that marro warriors are pink. Somone else says that they are not green. These two facts don't contradict, so we cant argue.

You say the chance of rolling for chomp once is 25%. They say the chance of rolling for chomp at least once, out of three tries is 37/64. These dont contradict, so there is no argument.

Or is this thier math? I haven't actually taken the time to verifiy thier math. Is it incorrect? either way, there is a way of caulculating the chance of rolling chomp at least once out of three tries.
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Old October 9th, 2007, 09:16 PM
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Browncoat Browncoat is offline
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In addition:

The reason for my interest in this in the first place is that when I draft and army, I avoid figures with D20 abilities like the plague. For the most part, I prefer units with "bread and butter" type attributes that I can more easily rely on, and not chance my battle to a roll of the D20.

That said, even though there have been posts saying that both theories are correct...I have to hold on to mine being "more" correct. You can't subscribe to the other theory because you don't know how many rolls it will take for a successful Chomp. Each roll must be treated independently, as if it were the first and last roll needed, at 25%. If you knew going in that it was going to take at least 3 rolls to be successful, then things would be different.

Their math is correct. I'm not debating that. But (unless I'm wrong) they are saying that in a Kaemon vs. Grimnak battle, Grimnak's success rate for Chomp makes him a bigger threat than Kaemon's "bread and butter" type stats.
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Old October 9th, 2007, 09:21 PM
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  #10  
Old October 9th, 2007, 09:22 PM
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a.2+2=4

b. 2.5+1.5=4

Which is more correct?

There is no such thing as "more correct" in math. You dont know that it will take one roll to be succesful, you dont know if it will take 100. It's a probability. Both theories are correct . <--Period
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Old October 9th, 2007, 09:25 PM
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Quote:
Originally Posted by Mooseman
a.2+2=4

b. 2.3+1.5=4

Which is more correct?

There is no such thing as "more correct" in math. You dont know that it will take one roll to be succesful, you dont know if it will take 100. It's a probability. Both theories are correct . <--Period
Ah... B!
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  #12  
Old October 9th, 2007, 09:36 PM
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Browncoat Browncoat is offline
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Okay, I see your point. However! See, there had to be a catch...

If both are correct, and apparently they both are, how does that apply to the game itself?

Grimnak's card reads that you need 16-20 for a successful Chomp roll against a unique hero. This translates to the 25%.

Grimnak's card does not read that if you are unsuccessful on your first Chomp roll, that you may roll again. This translates to the other theory of 43.75% after two rolls.

My theory: Remains constant. Other theory: Can only be applied after a failed attempt. I suppose that this is where the gambler's part comes in. Which unit would you put your money on? This all comes back to the army I posted, and how it would hold up in battle.
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