Ask the Wizard #143

The probability of hitting all 20 is 1 in combin(80,20) = 3,535,316,142,212,180,000. So the odds are more like 3.5 quintillion to one. Assuming 5 billion people on earth, and they all played once a week, there would be one winner every 13.56 million years on average. Most casinos pay the same amount for hitting close to 20. For example the Las Vegas Hilton pays $20,000 for hitting 17 or more out of 20. I have never heard of anyone every hitting 20 out of 20, and doubt very much that it has ever happened.

Okay, a suited 5/6 against pocket aces, both of different suits, will win 22.87% of the time, tie 0.37%, and lose 76.75%. A suited 6/7 will win 22.88%, tie 0.32%, and lose 76.80%. So the suited 6/7 will win 0.01% more. However the suited 5/6 is better because it ties 0.05% more. The reason for this seems to come down to the straights. There are going to be more waits to form a straight on the board if all the mid-cards in left in the deck. Removing a 7, as opposed to a 5, makes it more difficult to make straights with the remaining cards, thus making ties less likely, and thus the expected value less.

The probability of A is obviously 25%. The probability of getting zero shots out of five is 0.95⁵=77.378%. So the probability of getting at least one out of five is 100%-77.378%=22.622%. So A has the higher probability.

The odds are the same. However it will be less volatile for both of you to play at half the bet size.

First, whoever accepted this bet should honor it, on principle alone. A gentleman honors his debts, especially gambling debts. Second, although I haven't studied it I think the quarters may actually be negatively correlated. For example if the first quarter has a low total it may be more likely that either team will have good field position at the beginning of the second quarter, and thus likely to make the second quarter high scoring, and vise versa.

Before considering your own cards the probability is 4×combin(13,3)/combin(52,3) = 5.1764706%.

Another way to look at it is the probability second card in the flop will match the first in suit is (12/51). The probability third card in the flop will match it is (11/50). (12/51)×(11/50)=5.1764706%.

The odds change a little if you consider your own cards. If you have two cards of the same suit, then the probability of a suited flop is pr(flush in same suit) + pr(flush in a different suit) = combin(11,3)/combin(50,3) + 3×combin(13,3)/combin(50,3) = 5.2193878%.

If you have two cards of a different suit, then the probability of a suited flop is pr(flush in suit in common) + pr(flush in a different suit) = 2×combin(12,3)/combin(50,3) + 2×combin(13,3)/combin(50,3) = 5.1632653%.

She might be using you as her psychiatrist. It sounds like she is leading you on and just wants somebody to listen to her. Another possibility is she is in another relationship that is rocky and you are her backup plan. You can’t waste your time in limbo indefinitely. I would tell her to not contact you until it is with a meeting date.