Ask The Wizard #248

What is the single loosest video poker game in Vegas?


To the best of my knowledge, the loosest video poker game in Vegas is the 101.60% 5¢ Loose Deuces game at the Fitzgeralds. It is located upstairs, near the sports book.

Update: This answer was correct at the time of writing. However, said machine has since disappeared. See my Ask the Wizard #292 for the new loosest video poker machine in Vegas.

What is the probability of two bingo cards in play in the same session being identical?

Tara from Vashon, WA

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.

I was recently playing in a casino in London where they offer the "Egalite" total side bets in baccarat. These are bets that the banker and player tie at a specific total. Here are the payoffs:

  • 0=150-1
  • 1=215-1
  • 2=225-1
  • 3=200-1
  • 4=120-1
  • 5=110-1
  • 6=45-1
  • 7=45-1
  • 8=80-1
  • 9=80-1
What is the house edge for each of these bets?


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.

What is the probability of an onside kick being successful in the NFL before the 4th quarter. I mean, the move in the Super Bowl was absolutely brilliant, but did the Saints coach have the stats to back up his decision, or was he just going on a hunch?


According to an outstanding article at, 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.

What video poker game has the highest hit frequency?

James from Las 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.

Video Poker Return and Hit Frequency

Game Return Hit Frequency
Deuces and joker wild 0.990675 0.503768
Tens or better 0.991390 0.494518
Bonus Poker 0.991660 0.455145
Jacks or Better 0.995439 0.454565
Double Double Bonus 0.989808 0.447163
Deuces wild 0.994179 0.442807
Joker poker 0.984425 0.441435
Double Bonus 0.991065 0.431893
One-eyed jacks 0.989562 0.370122
Royal aces 0.991981 0.300874