What are the odds of rolling 2?

If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.

thoughtco.com - Probabilities for Rolling Two Dice - ThoughtCo

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One popular way to study probability is to roll dice. A standard die has six sides printed with little dots numbering 1, 2, 3, 4, 5, and 6. If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on. But what happens if we add another die? What are the probabilities for rolling two dice?

Dice Roll Probability

To correctly determine the probability of a dice roll, we need to know two things: The size of the sample space or the set of total possible outcomes

How often an event occurs

In probability, an event is a certain subset of the sample space. For example, when only one die is rolled, as in the example above, the sample space is equal to all of the values on the die, or the set (1, 2, 3, 4, 5, 6). Since the die is fair, each number in the set occurs only once. In other words, the frequency of each number is 1. To determine the probability of rolling any one of the numbers on the die, we divide the event frequency (1) by the size of the sample space (6), resulting in a probability of 1/6. Rolling two fair dice more than doubles the difficulty of calculating probabilities. This is because rolling one die is independent of rolling a second one. One roll has no effect on the other. When dealing with independent events we use the multiplication rule. The use of a tree diagram demonstrates that there are 6 x 6 = 36 possible outcomes from rolling two dice. Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die.

Probability Table of Rolling Two Dice

The possible outcomes of rolling two dice are represented in the table below. Note that the number of total possible outcomes is equal to the sample space of the first die (6) multiplied by the sample space of the second die (6), which is 36.

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Can a dealer go past 17 in blackjack?

In most casino blackjack games, a dealer must take a card if he hits 16 or below and stand at 17 or above. Some tables, though, say the dealer must hit soft 17, meaning he has a chance to increase his score up to 21.

edge.twinspires.com - What to do when the dealer hits soft 17 in blackjack | The TwinSpires Edge

Blackjack is a simple game to play, but most novices wrongly believe following a solid blackjack strategy must be hard. That’s far from the case. The simple rule, which will improve your win rate, is that when the dealer looks weak, with a poor upcard, you can stand on more cards, and when the dealer looks strong, you should look to get your total higher and take more risks. It’s a fact that the house edge in blackjack can be as high as 4-5% for a poor player. But that tumbles to as low as 0.5% if you play a sound strategy. However, even experienced blackjack players can make strategy mistakes, especially when it comes to how the dealer plays a soft 17.

What is soft 17 in blackjack?

An ace is worth either one or 11 in blackjack. That means when you have two cards, and one is an ace, you have a choice of totals to work with. If, for example, you have an ace and a three, you have either a total of four or 14. You can take a card and then decide which total to use after that. You become accustomed to how to play soft aces soon enough. But what about the dealer? He can play soft aces just the same as you. But there is one significant difference. In most casino blackjack games, a dealer must take a card if he hits 16 or below and stand at 17 or above. Some tables, though, say the dealer must hit soft 17, meaning he has a chance to increase his score up to 21.

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