A Brief Lesson on Probability
Posted June 3rd, 2010 at 06:47 PM by Sujoah
(A brief note before I begin: During 7th and 8th grade, I took a math class after school called MEGSSS. It also took place in the summer. I enjoyed the summer sessions, and hated the schoolyear ones. The Probability class took place in the summer of Year 2. (Another note: This is something for people in the St. Louis and St. Charles area.) (Hey look, a third note: The books we used for the class were books in the Elements of Mathematics series. I wouldn't recommend buying these books for yourself, they are written very oddly and hard to understand unless you have already learned what they're talking about.))
Probability. It's used a lot in the world, and also in Heroscape. And I'm going to talk about it because I have nothing better to do.
It's pretty easy to figure out that if you flip a regular coin, that the odds of it being heads or tails would be 5050. And with a regular die, each number has a 1/6 chance of showing up. But what if you flip two coins? Then you have a 25% chance of each o the following: HH, HT, TH, TT (heads being H, tails being T). But now you want to get two of the same side in a row. And the odds of that happening is 50%. you may be thinking, "No it wouldn't, because there's a 50% chance of the first one, and a 50% chance of the second one, giving you 25%." But that's actually wrong. You don't care what the first result is, just as long as the second one matches. So, the first coin must be either H or T. 100% chance. And the second must match it. 50% chance. And when multiplied, you would get 50%. Same with rolling doubles on a 6 sided die, or you and your opponent rolling the same initiative number at the start of a round. You get something, and they need to match it. That's it.
Now, for them to both be the same, you would need to multiply both chances. So, if I want to get two 20s, then I would have a 1/400 chance. Not very likely, but the exact same odds of getting a 7 then an 18, or a 4 and a 19, or whatever.
There are also times when you would add the numbers instead of multiplying them  when they don't depend on each other. Say you need to roll at least a 16 to let your Vipers take another turn. the odds of getting a 16 exactly are 1/20, as are the odds of a 17, an 18, a 19, and a 20. So you would add them: 1/20 + 1/20 + 1/20 + 1/20 + 1/20 = 5/20, or 1/4.
And that's it for now. I might do another one of these on number theory, as that was the other class that we took during the summer of Year 2.
Probability. It's used a lot in the world, and also in Heroscape. And I'm going to talk about it because I have nothing better to do.
It's pretty easy to figure out that if you flip a regular coin, that the odds of it being heads or tails would be 5050. And with a regular die, each number has a 1/6 chance of showing up. But what if you flip two coins? Then you have a 25% chance of each o the following: HH, HT, TH, TT (heads being H, tails being T). But now you want to get two of the same side in a row. And the odds of that happening is 50%. you may be thinking, "No it wouldn't, because there's a 50% chance of the first one, and a 50% chance of the second one, giving you 25%." But that's actually wrong. You don't care what the first result is, just as long as the second one matches. So, the first coin must be either H or T. 100% chance. And the second must match it. 50% chance. And when multiplied, you would get 50%. Same with rolling doubles on a 6 sided die, or you and your opponent rolling the same initiative number at the start of a round. You get something, and they need to match it. That's it.
Now, for them to both be the same, you would need to multiply both chances. So, if I want to get two 20s, then I would have a 1/400 chance. Not very likely, but the exact same odds of getting a 7 then an 18, or a 4 and a 19, or whatever.
There are also times when you would add the numbers instead of multiplying them  when they don't depend on each other. Say you need to roll at least a 16 to let your Vipers take another turn. the odds of getting a 16 exactly are 1/20, as are the odds of a 17, an 18, a 19, and a 20. So you would add them: 1/20 + 1/20 + 1/20 + 1/20 + 1/20 = 5/20, or 1/4.
And that's it for now. I might do another one of these on number theory, as that was the other class that we took during the summer of Year 2.
Comments 3
Total Comments 3
Comments
Thanks for sharing. I had to correct my advanced math teacher (Algebra) about the part involving trying to get doubles on a coin. Probability is something very important in the world and a lot of people who take chances don't realize these probabilities.
Probability is extremely imporant in Heroscape so this blog should help newbies a little bit. 

Posted June 3rd, 2010 at 08:29 PM by rednax 
I was atually taking a test when I thought of doing this. Because I was getting a lot of answers that were the same as the one before it, then I remembered that it would still have a 1/4 chance of matching the one above it.


Posted June 3rd, 2010 at 09:31 PM by Sujoah 
I'm really not one to try to bump things, but I really do wonder who someone who is banned can generate more discussion than probability.
Probability says that it's not likely. And yes, I do sometimes refer to things as though they are deities. I'm weird like that. 

Posted June 6th, 2010 at 09:24 PM by Sujoah 
Recent Blog Entries by Sujoah
 Heroscape  A Game that will Never Die (November 3rd, 2010)
 Rawr! (September 3rd, 2010)
 Random Note (July 13th, 2010)
 A Brief Lesson on Probability (June 3rd, 2010)
 The Power of Yoink (February 11th, 2010)