# Ask the Wizard #159

Back in 2002 you answered a question about Washington State and commission free pai-gow, or fortune pai-gow as it’s called, saying that since the house always banks, the house advantage is 1.44%. Well, they do allow player banking with commission free pai-gow, so how does that now effect the house advantage?

Michael from Marysville

According to my sources in Washington state many casinos waive the 5% commission if the player makes the Fortune side bet. The most common pay table for the Fortune bet in Washington I’m told is 2/3/4/5/25/50/150/400/1000/2000/8000, which has a house edge of 7.83% less 1.07% for each additional player at the table. So the expected loss of a $5 Fortune bet is 39.14 cents less 5.34 cents for each additional player. The following table shows the breakeven point between making and not make the Fortune bet according to the number of players at the table, including yourself.

- 1 player: $27.36
- 2 players: $23.63
- 3 players: $19.90
- 4 players: $16.17
- 5 players: $12.44
- 6 players: $8.71
- 6 players: $4.98

For example, if there are four players (including yourself) you should make the Fortune bet if your pai gow poker bet is $17 or more, and not if it is $16 or less.

For in-running betting, if a tennis player has a chance "p" of winning a game, what chance does he have of winning a set?

Mike from Perth

As I understand the rules of tennis the winner of a set is the first to win six games, and by a margin of at least two games, except a 6-6 tie will result in a single tie-breaker game. The following table shows the probability of winning a set, given the probability of winning a game.

### Probabilities in Tennis

Probability Game Win |
Probability Set Win |

0.05 | 0.000003 |

0.1 | 0.000189 |

0.15 | 0.001899 |

0.2 | 0.009117 |

0.25 | 0.028853 |

0.3 | 0.06958 |

0.35 | 0.138203 |

0.4 | 0.23687 |

0.45 | 0.361085 |

0.5 | 0.5 |

0.55 | 0.638915 |

0.6 | 0.76313 |

0.65 | 0.861797 |

0.7 | 0.93042 |

0.75 | 0.971147 |

0.8 | 0.990883 |

0.85 | 0.998101 |

0.9 | 0.999811 |

0.95 | 0.999997 |

The formula for any probability of winning a game p, and losing q, is 1*p^{6} + 6*p^{6}*q + 21*p^{6}*q^{2} + 56*p^{6}*q^{3} + 126*p^{6}*q^{4} + 252*p^{7}*q^{5} + 504*p^{7}*q^{6}

I am continued to be amazed at the number of personal relationship questions your readers ask. Your answers are spot-on, as far as I am concerned, but does it surprise you that you have become a modern-day "Dear Abby"? Maybe there is a correlation between solving complicated math problems and solving complicated matters of the heart?? In any case, keep up the good work.

Scott from Pittsburgh

Thanks for your vote of confidence. According to my count I only received four such questions in the first 134 columns. However starting in August 2005 they flooded in, partly because my webmaster, Michael Bluejay got us the #1 rank in Google for a search on "Is my boyfriend cheating on me". We have since dropped to #2. To answer your question, yes, there is a connection. I take a cold calculating look at both casino games and life. When I give advice in either venue it is based on what I think will make the asker happier in the long run.

Which casinos in Las Vegas gives the best odds on Craps.

Wayne from Honolulu

The Casino Royale, which offers 100x odds. For complete playing conditions in Vegas please see my new Vegas craps directory.

Re buy bet vig. in craps. Most online casinos on a $10 4/10 buy bet return 19.00, they claim a 5% vig. I always thought this was on the bet amount, not on the win amount which means the return should be 19.50 which is how Bodog does it. Are the other casinos wrong?

Al from Calgary

Yes. Assuming the commission is paid only on a win then it should be applied to the bet amount, not the win amount.

Me and my boyfriend have been together for a little more than a year. i am 18 as well as he. i am 8 months pregnant. my problem is that in december, my boyfriend went to puerto rico with his family for his sisters birthday (because that is where his family lives). he came back down in january and i had already moved in. since he has come back we have done nothing but argue. it all started when we developed a camera with all pictures of him and one girl. after a few days, i got over it and figured that she was just a friend. but then i found and address to puerto rico in his wallet and when i asked him what it was, he told me it was hers. we argued for days and he told me that she was nothing but a friend and he throiugh the address away. Here is my problem, YESTERDAY, i found the address again hidden in his wallet, but this time on different paper. when i asked him why he keeps wrting it down and putting it in his wallet he tells me she’s just a friend and that he hasnt written to her. what should i do. i am trying my hardest but i cant understand what he is doing, or what i am doing to him to make him do this. does he even understand that he has a child due in april??? please give me some advice

Amanda from Woonsocket

This is not a good time to be turning a small problem into a big one. Your evidence that there is anything going on between him and this other girl is pretty light. If you want him to be around for you and the baby then be nicer to him. All this nagging about an address in his wallet is only going to drive him away, probably to Puerto Rico.

I have told you this before, but I love your site!!! I refer people to it all the time. I am a dealer in AC and am visiting Vegas again next month. I want to see the real dirt casinos when I come out... I mean a place where $15 player would have his feet washed!!! We are staying with friends who live outside Henderson... Any suggestions?

Jim from Atlantic City, NJ

My webmaster, Michael Bluejay, loves the dives too. He never misses a chance to visit the Western, although he laments, "That place has really gone uphill." Unlike the other low-end casinos of downtown, mainly the El Cortez and the Gold Spike, the air is not quite as thick with cigarette smoke at the Western. Closer to your friends I truly like both downtown Henderson casinos, the Rainbow Club and the El Dorado. Both are old fashioned and cater the low rolling locals. However both are clearly worlds above the Western. Here is Bluejay’s rundown of skanky Vegas hotels.

On TV they had a program the Do & Don’ts in Las Vegas. On this program they advised you that when playing Blackjack and win you are not subject to taxes?? I can’t believe this.

Mahalo

You are subject to tax for any gambling winnings. However table games players are basically on the honor system. An exception that a W2G form is generated if a win is 300 for 1 or more odds and is over $600. That is usually only an issue with progressive jackpots. Also, if there is a cash transaction of $10,000 or over the casino is obligated to fill out a CTR, which stands for Cash Transaction Report. Yet these are nothing to worry about, and I think many big bettors are overly paranoid about them.

me and my girlfriend ahve been going out for almost 15 months and at first she was OBSESSED!! with me and over the past month it seems like she doesnt even want to talk to me anymore and im now obsessed with her. I got her an ipod for valentines day and i was hoping that would work, bu it didnt help to much. What do i do?

David from Chicago

That is what can happen if you rush a relationship. It takes a while to truly get to know somebody. Next time take it slow and don’t fall in love until you truly know the other person well. An iPod, even crammed with love songs, is only going to get you so many points. My advice is to agree to a cooling off period of a month or two where you don’t see each other. Then after it is over, and it is mutually agreeable, try it again, but be more patient.

In your March 13, 2006 Ask the Wizard, you gave three formulae for the "rupee" game. While the solution is mathematically right, I can’t for the life of me understand how the three equations model the problem. Can you give any insight on how you came up with the three equations?

Rick from Covington, LA

I had a number of people ask me to expand on my answer. The solution requires basic matrix algebra.

Start by defining x as the answer, or the average number of flips until the disparity between heads and tails is 3.

Let y be the expected number of flips from a point where one side is up by one flip.

Let z be the expected number of flips from a point where one side is up by two flips.

After the first flip one side will be in the majority by one flip. So x=1+y.

When either side is one flip ahead another flip will result in either the initial tied state, or one side being up by two flips. Both outcomes are equally likely. So y=1+0.5*x + 0.5*z

When either side is two flips ahead another flip will result in either one side being up by one flip, or the end of the game. Again, both outcomes are equally likely. So z=1+0.5*y

So we have three equations and three unknowns:

(1) X= 1+y

(2) Y = 1+ 0.5x + 0.5z

(3) Z = 1+ 0.5y

To solve lets first get rid of the decimals by multiplying the last two equations by 2.

(1) X= 1+y

(2) 2Y = 2+ x + z

(3) 2Z = 2+ y

Let’s substitute 1+y, from (1) for x in (2).

2Y = 2 + 1 + y + z

(4) y = 3 + z

No substitute 3+z for y in (3)

2z = 2 + 3 + z

z = 5

Now substitute 5 for z in (4) to get

(5) y = 3+ 5 = 8

No substitute y = 8 in (1) to get

(6) x = 9

All other things being equal, in particular temperature and pressure, can a kicker kick a ball further in low or high humidity?

Anonymous

Physics is not my strong subject so I asked two physics experts, my father and Andrew N., this question. Both agree the ball will go further if the humidity is high. Here is how Andrew N explained why.

*Interesting question. I looked up a few bits of data on the internet, and it looks like the ball will go further on a humid day than on a dry day, everything else being equal. The two factors that are most relevant are: 1) the air density; and 2) air viscosity. *

1) Air Density

Contrary to popular belief, humid air is lighter than dry air. This is because the water molecules take up the same space but weigh less than the O2/N2 mixture. Lighter air results in less buoyant force on the football because the football is displacing less mass. However, the density of dry air at 20 C and 700 kPa(*) is 8.33 kg/m3, and with 42.1% relative humidity at the same temperature and pressure the density is 8.32 kg/m3 according to the sources listed, a difference of about 1/10th of 1%. So this isn't going to effect the distance much.

(*) - 700 kPa is a high pressure, but it's the only data I could find. However, in engineering terms it's not much different from normal atmospheric pressure so I believe the properties listed in the data will be applicable to the situation at normal atmospheric pressure (101.325 kPa).

2) Air viscosity

Viscosity is the force that contributes to skin drag on the football. A lower viscosity will contribute less to drag, resulting in a longer flight. For dry air at 20 C and 700 kPa, the dynamic viscosity is 18.3 Pa*s, while for the air with 42.1% humidity the viscosity is only 17.8 Pa*s. This is a difference of about 3%, again not much but a little more significant than the effect of air density. However, humid air will still contribute to a slightly longer football flight.

To see if this makes sense in the real world, I found a golf website that has some data on golfball flight distance in dry and humid conditions:

As you can see, in humid air the golfball goes further, but only by a yard or two at most. So humid air definitely results in a longer projectile (golfball or football) flight, but the effect is very slight.

Andrew N

Data culled from:

__wipos.p.lodz.pl/HighTech/example1.html"__ (data on humid air at 20 C and 700 kPa). Link no wonder works.

physics.holsoft.nl/physics/ocmain.htm (calculators for humid air properties)

**Wizard's comments**: To add to the first point, Boyle’s Law says that given the same temperature, the volume of gas is inversely proportional to the pressure. So given the same temperature and pressure the volume of gas will be constant, in other words the same number of molecules per unit area. The atomic weight of oxygen is 16, nitrogen is 14, and hydrogen is 2. So a water molecule (H2O) has an atomic weight of 18, while O2 and N2 are much heavier at 32 and 28 respectively. So when it is humid the lighter water molecules push the heavier O2 and N2 molecules out of the way, causing for less resistance for the football to cut through the air.