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Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large number says (in plain english) that the more you try (approaching infinity, that is), the closer your real outcomes will get to the theoretical probability, or expected value if you will. That is quite mindblowing, if you think about it but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. Now I tell you that if you flip it over and it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Why? Because the probability of it being an ace is 1 (or 100%) your potential winning is 100€ so 1 * 100€. Now what if you had two cards face down, and only one is an Ace? Three cards face down? Four? Seventeen? What is your expected value in each case?

Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large numbers says (in plain english) that the more you try (approaching infinity, that is), the closer your results will get to your theoretical probability, or expected value if you will. That is quite mindblowing if you think about it, but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. Now I tell you that if you flip it over and it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Why? Because the probability of it being an ace is 1 (or 100%) your potential winning is 100€ so 1 * 100€. Now what if you had two cards face down, and only one is an Ace? Three cards face down? Four? Seventeen? What is your expected value in each case?

Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large number says (in plain english) that the more you try (approaching infinity, that is), the closer your real outcomes will get to the theoretical probability, or expected value if you will. That is quite mindblowing, if you think about it but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. Now I tell you that if you flip it over and it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Why? Because the probability of it being an ace is 1 (or 100%) your potential winning is 100€ so 1 * 100€. Now what if you had two cards face down, and only one is an Ace? Three? Four? What is your expected value in each case?

Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large number says (in plain english) that the more you try (approaching infinity, that is), the closer your real outcomes will get to the theoretical probability, or expected value if you will. That is quite mindblowing, if you think about it but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. Now I tell you that if you flip it over and it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Why? Because the probability of it being an ace is 1 (or 100%) your potential winning is 100€ so 1 * 100€. Now what if you had two cards face down, and only one is an Ace? Three cards face down? Four? Seventeen? What is your expected value in each case?

Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 6 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large number says (in plain english) that the more you try (approaching infinity, that is), the closer your real outcomes will get to the theoretical probability, or expected value if you will. That is quite mindblowing, if you think about it but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. I tell you that if it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Now what if you had two cards face down, and only one is an Ace? Three? Four? What is your expected value in each case?

Probability: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has 4) is favorable.

Expected value is simply the product of the probability of something happenning AND the 'value' of that something. ( probability * value )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why? Because you are virtually winning the 4/52nd part of the 100€s every time you pick a card.

You could say that probability is just theoretical, but the law of large number says (in plain english) that the more you try (approaching infinity, that is), the closer your real outcomes will get to the theoretical probability, or expected value if you will. That is quite mindblowing, if you think about it but also makes a lot of sense.

Just thought of something even more simple: Let's say there is only one card, face down: an Ace. Now I tell you that if you flip it over and it's an ace, then you get 100€. How much is your expected value? Of course it's 100€. Why? Because the probability of it being an ace is 1 (or 100%) your potential winning is 100€ so 1 * 100€. Now what if you had two cards face down, and only one is an Ace? Three? Four? What is your expected value in each case?