What are the chances of... ?

Question

Okay, I am asking this question simply because my roommate and I argued about this all night..

Here's the scenario: Given two possible outcomes, what are the chances of each outcome? Assuming all else equal, it would be 50-50.

However, he says.. given any two outcomes, there is ALWAYS a 50-50 chance of each outcome. For example, I asked what the chances were of a professional basketball team beating a college basketball team? Based on the experience and skill level of the professional team, any logical person would say that the professional team has a higher chance of winning. But, my roommate is persistent in believing that there would STILL be a 50-50 chance of winning.

I have tried to persuade him by explaining that people would not bet on certain teams to win if there was always a 50-50 chance of winning. You must consider all other variables which would cause the outcome.. So, I need an objective opinion.. and perhaps a better example that what I gave.

Answer 1

Testicles

Answer 2

The guy is probably just trying to get a rise out of you.  

But he has a point in a sense that if you know nothing other than there are two possible outcomes, then there is a 50-50 chance of either one.  Once you know information about the mechanism behind the outcomes, you now have a conditional probability and the known probability changes.  You are also right, because usually there is more information than just the two possible outcomes.  Take the russian roulette example.  if I point a gun at your head and pull the trigger, what's your chance of dying?  If we know the gun is a six shooter with one bullet in it and the magazine has been spun randomly, then we know it's a 1/6 chance.  If we know I'm a successful serial killer and I mean what I say, then the chance is more like 100%.  If it's a random gun found on the street, then we would need to know the statistics on the chance that a randomly found gun is loaded.  If we know absolutely nothing, then we have to claim that the chance is 50-50 for two possible outcomes.  But once we know one shred of information, suddenly we can hone down our prediction based on our previous knowledge and give a new conditional probability.  Given that we're playing russian roulette, the chance is 1/6; given that I just stole it from a drug dealer, the chance is 9/10, given that I pulled the gun out of a wall mart display, the chance is 1/100.  

If I tell you there are two basketball teams, A and B, which one will win?  If you know nothing else, then you have a 50/50 chance of being right by guessing either one.  Pure 50/50 chance.  But now if I tell you that team A is my neighborhood kids, and B is a pro team, you know now that there is a 1/100000 chance that team A will win.  But what if that's the case, but you don't have that information beforehand?  You would still have to conclude that theres a 50/50 chance of either team winning and flip a coin to see which to bet on. Really what I'm doing is accepting that without information, I have a 50-50 chance of GUESSING right, not that there's a TRUE 50-50 chance that my chosen team will win. If everybody betting had the same info to start with then 50% would be right and 50% would be wrong.  But if everybody else knew that only team B was pro and you didn't, you'd have  a disadvantage in the bet.  You'd have a 50/50 chance of winning, and everybody else would have a 100% chance of winning.  

I guess the moral of the story is that knowing nothing about the conditionality of the events, there is always a 50-50 chance of guessing the correct outcome, even if the intrinsic probability is not 50-50.  You are thinking of the intrinsic probability--a pro team will beat the kids 100% of the time--if you know which team is pro.  your friend is thinking that if you don't know that information, you still have a 50-50 chance of guessing the winning team--predictive probability perhaps.  But once you know the background or conditional information, you can adjust the predicted probability and therefore your guess.  Knowing more information changes your probability of choosing the correct outcome, but it never changes the intrinsic result.

Answer 3

You can only say it's 50-50 when all of the variables are known. If I were to play basketball, I would almost certainly lose because I am not athletically gifted. If a team of nerds like me played a team of athletes, we would almost certainly lose for the same reason. Here the variables are not win/lose, they're win/lose, out of shape/fit, practice, etc.

So you're right to take into account skill and past statistics.

Conversely, if all variables are known and only two possibilities exist, the outcome is 50-50 either way. Schrodinger's cat (google it) is a great example.

Answer 4

Your roommate probably continues this argument only because he knows that it is getting to you.

Here is an analogy.  Let's say I have 2 Corvettes, and I take them to the drag strip.  What are the odds that Corvette #1 will win?  

If your roommate knew that one had a 300 HP engine in it , and the other had a 100 HP engine, he would not be expecting the one with the smaller engine to win 50% of the time.  In fact, I don't think he'd put any money on that car - ever.

Answer 5

Okay lets get straight exactly what was being discussed.  The thing in which we started out discussing was the basketball game.  I never said that in any situation with two outcomes that it is a 50-50 chance.  I said that in a sporting event between two teams, players, opponents etc. that the chances of one team winning and one team losing is 50-50.  Matt, your example with the pencil does not work because using prior knowledge everyone knows that the pencil will never float correct? so there is not a two possible outcome scenario.  In an effort to try and say one team is better then another you have to look at other variables.  However, just because one person's stats are better then someone else's does not mean that they have a higher chance of winning, and here's why.  Whenever you pull these stats you are using them for only a certain time period, are you not? and in doing so are you not neglecting prior stats to those.  If you are then why is it that you are able to use some stats in your analysis whilst others are not good enough for you.  Therefore, all stats must be thrown out unless you have the stats for their entire lives.  that is the only way to evaluate them on equal grounds because all variables change everyday.  Since stats are no longer able to be used in your pregame analysis, let's move on to some more things that someone might use to analyze a game.  Practice.  Practice is arbitrary and cannot be considered since you can not quantify what practice does to someone.  People spend hours upon hours in a gym and nothing happens, while someone can spend just one hour and be infinitely better.  So you cannot evaluate who is going to win by their quality of practice and the length of their practice.  How about health?  How can you say how much a sickness or injury is going to affect someone?  you can't.  So you cannot evaluate who is going to win by their health.  Since you have no basis to evaluate the two on they at the moment of the game are equal, regardless of whether or not one is pro or one is amateur at the beginning of the game their stats for the game are all the same, the score is the same and so on.  So each team has a 50-50 chance of winning the game.

Answer 6

Roll a set of dice.  Tell him there are two possiblities.  Either you will roll a 3, or you won't.  According to him, there is a 50% chance of rolling a 3.  This is obviously absurd.

Answer 7

just because there are two outcomes doesnt mean that there is always an equal chance. for instance, i'll use an example that even little kids can understand. say you have 20 socks, 18 white and 2 black, in a box. now, without looking  in the box, what is the chance of you picking a black sock? my seven year old brother is smart enough not to know its not 50-50 chance. and about the basketball games, obviously the person with the most experience would be more likely to win. if a person who never even touched a basketball played a professional player in  a one-on-one game, guess whos gonna win 99% of the times they play.

Answer 8

Here is what you do: get a pencil, hold it in your hand and ask your roommate "what is the chance that this pencil will drop to the ground when i drop it" tell him there are two possible outcomes 1) it does nothing (floats in the air) or 2) it falls to the ground.  if he says its 50-50, drop the pencil, continue to drop it until he realizes that no matter how many times its dropped, it will always fall to the ground. explain to him that there is a 100% chance that the pencil will drop, thus there is no 50-50 relationship.

If he doesn't like that example try this: a weighted coin gives 25% heads and 75% tails, this has been proven by flipping the coin 1 million times and then averaging the results together.  Therefore the next flip has a 25% chance of being heads and a 75% chance of being tails.

EDIT: So then break it down to a player on player level.  For instance the example to tell you friend: If i match micheal jordan (when he still played) against a random player from a NCAA division two team, who would win?  Obviously micheal jordan, being the best player since sliced cheese would win against little johnny nobody.  Thus the same disadvantage would exist for a team of NBA players against a team of NCAA players.  

Another example you could use is halo 3 competition. Is any two team match a 50:50 chance of winning for either team?  The answer is of course no, you can break down each team members stats, find their win percentage, average the entire team's percentages together and then you have a probability of one over the other.  The same can be applied to sports only, the calculation needed to compute the probability must take a wealth of other factors into consideration.