Ask the Wizard #18
Jim K. from Laguna Niguel, California
The number of ways to draw 3 cards out of the 47 remaining in the deck is combin(47,3)=16,215. One of those will be the three needed for a royal so the odds are 1 in 16,215.
Bry from Chesterton, Indiana
For other readers, let me explain that a put bet is making a pass or come bet after a point has already been established. The player may choose the point to be established on the put bet. While the player can make an odds bet immediately on top of the put bet, the opportunity to win on the initial roll is lost. The effect is the same as making a place bet or buying odds, but the house edge is different depending on the multiple of odds allowed. In the case of 20 times odds the house edge of the put bet on the 4 and 10 is 1.59%, on the 5 and 9 is 0.95%, and on the 6 and 8 is 0.43%. At this high level of odds allowed, which is much greater than the norm, all put bets are better than the corresponding place or buy bets. This option should never be taken at a casino that offers less than 5 times odds. At 5 times odds exactly, the put bet on the 6 and 8 is slightly better than the place bet. At 10 times odds or greater, all put bets become better than their corresponding place or buy bets. I shall add something to my craps section about the put bets, thanks for the idea.
Nathan from University, Mississippi
Good question. Unfortunately I don't have exact standard deviation figures according to specific sets of rules. The 1.15 figure on my site is based on liberal Vegas Strip rules. I agree that the double after split rule increases the standard deviation. Surrender would decrease it. Sorry I am not of more help than that.
Donna from Los Angeles, California
You're right, it is impossible for me to know without Microgaming giving me the details on how their reels are weighted. I have asked some of the major software companies for such information, but thus far nobody has volunteered anything. However, I can tell you that the average payback for all slots at the Golden Palace for the month of March 2000 was 95.67%. This information is available at the Golden Palace web site, click on the Price Waterhouse Coopers monthly payout review.
I have a number of questions. The first is about the banners. I'd like to know how we could optimize your income by clicking on the banners. Do you get paid on the basis of hits, unique hits or a flat fee or some other formula? Currently I only click on a banner if it's something new, but I'd be happy to click on a few banners every time I visit, if that would help generate income.
The next questions I have are about your perfect strategy for Jacks or Better table, and the practice Jacks or Better game. I hate to seem dense, but that's never stopped me from asking questions before. Where on the table do you find the rank of a hand with 1 high card (A,K,Q,J) and no penalty cards? My second question is somewhat related to the first. According to the practice game, the optimum play for a hand with unsuited A,Q,K and no penalty cards is to hold the K,Q and discard the A with the low cards. Intuitively, I would have thought that keeping the Ace is the better play. What is the advantage of dropping the Ace, and how would I determine the optimum play on this hand from the table?
Denis from Rochester, New York
Thanks Denis for your kind words and your interest to help keep the site financially healthy. When you first wrote just clicking my banners helped. However, as I update my answer in 2013, it is acquisitions that put rice on my table. It doesn't do much good to click on the banner if you don't at least sign up for an account, and preferably make a deposit.
You can see from my 9-6 jacks or better strategy, that there is a single line for "one high card." That is because an individual jack to ace is worth about the same.
Alex from Toronto, Canada
You have a legitimate point. At the time you wrote this I indicated the house edge according to a fixed set of rules that varied only by the number of decks. However, in real life, when single deck is offered the other rules invariably become more stingy. I have already enhanced the house edge table in the blackjack section to include a wider variation in rules. The typical Las Vegas single-deck game does not allow doubling after a split and the dealer hits a soft 17. With these rules, the house edge is 0.18%. The best single-deck game is at the Slots-a-Fun (next to Circus Circus) where the dealer stands on soft 17 for a player edge of 0.01%. Next door, at the Westward Ho, double after a split is allowed but the dealer hits a soft 17 for a house edge of 0.04%. About card counting, absolutely not, even the best of card counters will lose often. An entire month can be at a loss. Only over the very long haul does a net profit become likely.
Update: Since this writing the Westward Ho was torn down and the Slots-a-Fun has slots only.
- 4 decks
- 9-11 double
- one split only
- double after split allowed
- one card to split aces
- dealer stands on soft 17
- European card rule= none
- no surrender
Are these rules a good deal for me? What is the house edge? Thank you for an answer.
Kim from Helsinki, Finland
The house edge in this game is 0.51%.
Ric from Torrance, California
The probability of any royal flush is the number of possible royals, which is four (one for each suit), divided by the number of ways to choose 5 cards out of 52, which is combin(52,5)=2,598,960. So, the answer is 4/2,598,960 = 0.00000153908, or 1 in 649,740.
The probability of a sequential royal flush equals (number of suits) * (number of directions) / (total permutations of 5 cards out of 52) = 4 * 2 / permut(52,5) = 8 / 311,875,200 = 8 / number of possible royals, which is four (one for each suit), times the number of directions it can be in divided by the number of ways to pick 5 cards out of 52, which is permut(52,5)=311,875,200. So, the answer is 4/311,875,200 = 0.00000002565, or 1 in 38,984,400 .
d from Monterey, California
Alter then so that one die has a six on every side, and the other one has all ones and fives.
Dave from Redding, California
To become an actuary one must pass several examinations. The first set of exams are mathematically intensive and the second set are based on the theory of investments, actuarial science, pensions, and other such topics. However it will be difficult to find employment without a college degree. Most actuaries have at least an MA in mathematics. Your Microsoft certification would certainly give you bonus points but not enough to compensate for a lack of a degree. To learn more visit the Society of Actuaries web site.
Update: Since this question was posted the Society of Actuaries changed the exam requirements. There are now fewer but harder exams. That is about all I know about it.