Philosophical approach to probability

Say there is a card game with 2 cards X and Y. The rules say you must only flip over one card. There is a 99% chance that flipping over X will win you the game. The game is played once.

The question I would like to ask is, "How much does confidence affect the outcome of a one-time random event?"

Given that there is a 99% chance to win by flipping over X, it would seem sensible to flip that card. However, what does it mean to have a 99% chance (or any other chance) to win in a one-time event? There are only have two outcomes: win or lose.

>>1
It means that I would choose the card that I know to have the higher probability knowing that there is a 1/100 chance I'll be wrong. If I am wrong, oh well. You can't control randomness like that.

Confidence in X doesn't mean X is definitely going to be the winning card.

This and only this event, when there is no additional data, is going to be 50/50 X or Y.  Changing the probability means you have data from previous games that suggests X is 99% more likely to be a winning choice.  This would require 100 games to be played, with one of them actually having Y as the winner (if I remember correctly).

>>3
You don't necessarily need to play 100 games to know your chances. It is just inherent to the game.

It seems intuitively evident that knowing your chances won't change the nature of the card you pick. However, it does make a difference doesn't it? If say X had a 51% chance to win rather than 99%, you would be a little less comfortable picking it. So then, is the difference only just in your head?

can probability exist wihtout being in numerical form?

>>5

Certainly.  Probability exists independent of its observation by mathematical human eyes.  Consider an uneducated native in some backward part of the world who's never seen a book, much less numbers.  Such a person can still look up in the sky, see dark clouds, and recognize that it's probably going to rain.

>>1

It means that, on average, out of 100 trials, 99 trials will win on flipping X and 1 trial will not win on flipping X.  That's all it means.  The notion of trials seems pretty integral to the percentile approach to probability--- the fact that there are two possible outcomes is orthogonal to the probability of one or the other.

"However, what does it mean to have a 99% chance (or any other chance) to win in a one-time event?"

Probability is an observed property, it occurs as much as any other concept used to define observal properties of the universe. Probability is a mathematical concept (observed property) which measures the rate of possibility of something occurring and is determinned by prior observation of the said occurance.

We could go on and on for hours exploring how the mind "understands" abstract concepts etc.. but no.

I like cheese.

Probability is a function of what you know.  You obtain knowledge through observation.  However, let's say that before the game, a computer generates a random integer between 1 and 100.  If the number is 100, Y wins; if the number is 1-99, X wins.  If we think of it in this way and if we assume that the player knows the odds, the game is equivalent to the following guessing game:

1. A random number between 1 and 100, unknown to the player, is selected.
2. The player chooses a winning condition: either he wins if he guesses the correct number (equivalent to picking the Y card) or he wins if he guesses a number that is not the correct number (equivalent to picking the X card).
3. The player makes his guess.

We can see that even in a real-life case where the player knows the odds, he clearly has a 99% chance if he chooses X, and a 1% chance if he chooses Y.  Now, let's look at the same guessing game, only this time the player won't know the probability:

1. A random number between 1 and 100, unknown to the player, is selected.
2. The player picks either winning condition X or winning condition Y.  Since the player doesn't know that he has a better chance of winning with condition X, and probability is a function of what you know, we can assume that there is a 50% chance that he will pick each condition.
3. The player guesses his number.

The odds of winning this game then are (50% * 1%) + (50% * 99%) = .5% + 49.5% = 50%.

If knowing the odds makes the player /any/ more likely to pick X over Y (a fair assumption, I think), then the player's odds are increased over 50%; therefore, given that benign assumption, knowing the odds increases his probability of success.

Probability is a function of what you know.  Therefore, the more you know, the more accurately your probabilities will reflect the behavior of actual phenomena.  Knowing more, then, means that you will make better decisions overall.

bump

ITT: People who don't know shit about probability.

Y(ou) all lost the game.
Get it?

>>11
also kids who think they are geniuses

confidence affects that specific event at 0.01% where action is equal to 99.9%. The experience will either increase or decrease confidence thereafter and have an effect if there is a similar event. Thus, wtf, why are we talking about this probability garbage any way?