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Ask the Wizard #272

Did you bet on your namesake, Shackleford, to win the Preakness?

Todo el Mundo

Unfortunately not. My reason is that I thought the world was going to end that day, May 21, 2011, so I didn't think I would have enough time to spend any winnings.

What is 48/2(9+3)? A lot of forums are having a heated debate on this.

iamthepush

In evaluating mathematical expressions you use the following order of priority:

  • Parenthesis (what is inside them)
  • Exponents
  • Multiplication and division (equal priority)
  • Addition and subtraction (equal priority)

After this narrowing down, if you have terms of equal priority, then you go left to right. So, in this case we evaluate the parenthesis first, resulting in 48/2 × 12. Division and multiplication are equal in priority, so we do the division first, because it is furthest left. That gives us 24 × 12=288.

I have to go on record as saying that while I feel that 288 is the right answer, the syntax of the expression is terrible. It never hurts to put in extra parenthesis or brackets for clarification. I would have expressed this as (48/2) × (9+3).

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

At the City of Dreams casino in Macau they have an "any hardway" bet, which pays 4 to 1. What is the house edge on that?

stompi

I get a probability of winning of 2/11, for a house edge of 9.09%.

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

The story goes that some people believed that Friday the 13th was unlucky because it seemed the 13th of the month occurred more often on Friday than on any other day of the week. Does the 13th really occur on Friday most often or not?

Doc

I have to admit my initial answer to this question, in my forum, was wrong. There are 14 different calendars only, seven for each day of the week the year starts on, by two for whether or not there is a leap day. I incorrectly thought that there would be a 2800-year balanced cycle. However, that is not the case.

Before going further, let's review the leap year rules:

  1. Years evenly divisible by four are leap years, except...
  2. Years evenly divisible by 100 are not leap years, except...
  3. Years evenly divisible by 400 are leap years.

If it were not for the third rule there would be a nice 700-year cycle. However, the 400-year rule breaks the 700-year balanced pattern, and starts it over from the starting point. So there is a 400-year cycle, but it isn't balanced. The following table shows how often the 13th of each month falls on each day of the week in a cycle.

13th of the Monthby Day of the Week

Day Total
Sunday 687
Monday 685
Tuesday 685
Wednesday 687
Thursday 684
Friday 688
Saturday 684
Total 4,800

The average number in a cycle is 685.71. However, Friday exceeds the average at 688. So, every 400 years we get 2.29 extra Friday the 13ths.

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

Do you have any comment on the guy who recently won $15 million in Atlantic City?

Wizard's Father

To me, the key clue is this sentence from the article, "'They also agreed to discount 20 percent of his blackjack losses as an incentive to get him to play,' he said." With liberal blackjack rules, a well-financed player can easily have a strong advantage with a 20% rebate.

The proper strategy is to quit when you have either achieved a huge win or a moderate loss, whichever comes first. For example, winning $1,000,000 or losing $100,000. Most of the time you will lose, so it takes a big bankroll to weather the ups and downs. Fortunately for the player, he was properly financed to take advantage of such offers. Besides having an advantage, he may also have exceeded expectations since December. I salute him for his success.