What is the chances of being dealt a royal flush or a straight?

What is the chance of being dealt a straight (but not a royal) flush or better?

What are the chances of being dealt a hand that will lose to four of a kind.

To determine the chances of being dealt a royal flush or a straight flush, we first need to know the total number of possible poker hands and the number of favorable outcomes.

1. Total possible poker hands: There are 2,598,960 possible combinations of five cards from a standard deck of 52 cards.

2. Royal Flush: This hand consists of the Ace, King, Queen, Jack, and Ten of the same suit. There are only 4 possible royal flushes (one for each suit).

3. Straight Flush: This hand consists of five consecutive cards of the same suit (e.g., 2, 3, 4, 5, 6 of hearts). There are 36 possible straight flushes since there are 9 possible starting cards (Ace through 10) for each suit.

To calculate the probability, we divide the number of favorable outcomes (royal flushes + straight flushes) by the total number of possible outcomes:

Probability of royal flush or straight flush = (Number of royal flushes + Number of straight flushes) / Total possible hands

Probability = (4 + 36) / 2,598,960
Probability ≈ 0.000015391

Therefore, the chances of being dealt a royal flush or a straight flush are approximately 0.0015391%.

To determine the chances of being dealt a straight flush (excluding a royal flush) or a better hand, we need to exclude the 4 royal flushes from the favorable outcomes:

Probability of straight flush or better = (Number of straight flushes + Number of better hands) / Total possible hands

Probability = (36 + Number of better hands) / 2,598,960

Unfortunately, we can't provide an exact number for the "Number of better hands", as it depends on which additional hands you consider "better." However, it would be a combination of other high-ranking hands like four of a kind, full house, etc. To calculate this probability, the specific number of better hands needs to be known.

The chances of being dealt a hand that will lose to four of a kind can be calculated by subtracting the probability of having four of a kind (any rank) from 1. The probability of getting four of a kind depends on the specific rank being considered and the number of ways it can be formed.

Probability of losing to four of a kind = 1 - Probability of getting four of a kind