Sunday, December 12, 2010

Certainty ; Probability ; Sports ; but first, why does no one love me ='(

Comments? Is all I ask. Comments.

On the other hand, math class is good for philosophical thought; then needing to race the white board eraser to catch up on notes.

Yes, I did remove the word 'it' on purpose.

How sure can you be about something? How unsure can you be? This was the topic of a conversation that lead me to me believing I was correct and my conversational partner not admitting I was right; or atleast this is how I view the events. I'm sure she may disagree, or perhaps just not admit she agrees.

My Math teacher has given me the answer to this, or atleast agreed with me but gave me a numeral value to assign to it. My opinion was you could not be more than 100% sure. If you are 100% sure about something, then you believe it will happen. If you are, lets say, a bazillion percent sure of something, you are still only sure that this event will happen. Lets look at this in terms of probability for a moment.

If you are 100% sure, your probability is 1. It will happen. If you are more than one hundred percent sure, it will still happen. There is no being more guaranteed than it will, without question happen. Therefor, your probability is also only 1.

The same goes for uncertainty. You can be 0% certain, and know a given event will not happen. If you are -96% sure, or any other negative number, your certainty is still stating it will not happen. Your certainty is 0%, or 0 chance.

This leads to my Math teacher's explanation. When probability was being introduced she said proved, through numbers, that probability exists within 0 <_ x <_ 1 . <_ being 'less than or equal to' and x being probability. I would love to use the actual symbol but Blogger hates alt codes aparently, and everything else that's fun in situations like this. Oh well. If you don't understand, please ask.

And just because I thought of this... >_ is greater than or equal to. >_> is not greater than or equal to or greater than. It is mild frustration or displeasure.

I feel like that was all stated poorly. Probability can be expressed in a percent of 0% to 100%. There is no less than 0%, there is no greater than 100%. These percentages could also be considered to be 0 (0%) and 1 (100%). Probability, is the same as certainty. You cannot be one billion percent sure about something.

Lets have a rough topic transition and start flipping coins. Lets say you flip a coin twice. Your chances are 1/4 that you will get heads twice in a row. This is due to your first flip having two possibilities, heads or tails. If it is heads and you flip the coin again then it has two possibilities again. You could have HH, or HT. The same goes for if the first flip is a T (tails, as you may of guessed), and the second flip could be H or T. This leaves you with the four possible situations of HH, HT, TH, TT.

This is so much easier to explain graphically, but I don't have the time to do so at the moment.

What I would like to note in this, is the second flip still has an equal chance of being a H or a T. The first flip has a 1/2 chance, the second has a 1/2 chance, the billionth flip will have a 1/2 chance. By the time you reach a bazillion flips though, you will have an astronomical number of possibilities of which I don't want to figure out how many there are. Is bazillion even a proper number? Anyways, getting a desired number of 'wins,' or H's in a row becomes more unlikely the more desired wins there are. Each event has the same probability.

How does this size up to sports however? I feel very clever, using the phrase win as foreshadowing, even if the shadow was only cast over twenty-six words until the key phrase of sports was used. This also relates to gambling, especially if the cards are replaced and/or shuffled each time.

Lets say you're playing soccer, and you win one game. Your chances of winning the next game are just as likely, however your chances of winning two games in a row are half of winning just one (assuming the teams are evenly matched). This may seem a bit contradictory but I feel as if I have explained the mechanics behind this well enough. This situation is even more accurate for some gambling games, such as rolling dice. There is (assuming) no skill in rolling dice, and the number will be random. Each number should be just as likely as any other number to be the outcome (due to the sum of each opposite side of the dice adding up to seven; hence the idea of an evenly balanced dice; hence the idea of a weighed dice, or a dice that is more likely to land on a certain number), so each roll, or event, will have an equal chance of happening. Getting the same number twice has a 1/6 chance (first roll does not matter what number, second roll has a 1 in 6 chance of matching up to the first), and getting a desired number twice in a row has a 1/36 chance (1 in 6 times 1 in 6, or (1/6)x(1/6)=1/36).

With this said, this should mean if you are on a 'winning streak' that probability should be considered. You should not do anything different (still assuming each team is equally skilled), because your chances of winning the next game is the same as winning the last.

But in sports, such as soccer, each team is not equal. There are several variables that must be considered, a very influencing variable being skill. If you are winning a series of games, chances are you are going to continue to win that series because clearly you are doing something right.

Well that's kind of lame, now that I'm finished putting all of this idea together this concept does not seem all that great or worth sharing. This was another idea that occurred to me several years ago but it was not until recently that I was able to expand on it a bit and tell everyone who doesn't care about it. Now that I am done, I realize the time and how I have Act IV of The Crucible to read before I go to sleep. I'm rather tired now.

This was also my first real entry into my Idea Book that I received from Vortex. Speaking of aliases, next post I may be introducing, or reintroducing, a new alias. I almost wish I could end this like the last few seconds of each Pokémon episode.

Tune in next post to join Bugwords and the ramblings of his mind as he sets forth to defeat the next thought worth sharing to the world. > To be continued.

> Bugworlds.

Ah great, now I have the Pokémon theme song stuck in my head. Today I had a mind blowing moment. A reoccuring line the the theme song is "Gotta catch them all" or "gotta cattchum all" and the main character of the show is Ash Ketchum... Woah.

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