Ask the Wizard #248

It depends on how many cards there are in play. Assuming c cards in play, a good approximation for the probability for at least one set of identical cards is 1-e^{(-c/471,000,000)}. For example, with 10,000 cards in play, which I think is about right for a Vegas bingo session, the odds of at least one set of identical cards are about 1 in 47,000. To have a 50/50 chance of at least one set of identical cards, you would need to have about 330 million cards in play.

The house edge ranges from a low of 6.39% on a 7 tie, to a high of 12.45% for a 0 tie. I show the probability of winning and expected return for all ten bets on my baccarat page.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

According to an outstanding article at advancedfootballanalytics.com, the historical probability of success is 26%. However, with most onside kicks, the other team is expecting it, which lowers the probability of success. For surprise onside kicks, the probability of success is 60%! The thrust of the article is that smart strategy would be to do surprise onside kicks more often. I agree; it was a brilliant move by the Saints.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Counting a win of 1 as a "hit" (although it is really just a push), as far as I know, the highest hit frequency is in Deuces and Joker Wild. The 99.07% pay table has a hit frequency of 50.38%. The following table shows the hit frequency of various games. Not that you asked, but as far as I know, the lowest is Royal Aces Bonus Poker at 30.09%, which starts paying at a pair of aces.