Ask The Wizard #159

My information from various contacts in Washington indicates that many casinos do not charge the standard 5% commission if players choose to bank during their game. Fortune side bet I've learned that the prevalent payout table for the Fortune bet in Washington features numbers like 2/3/4/5/25/50/150/400/1000/2000/8000, leading to a house edge of 7.83%, which decreases by 1.07% for each additional player at the table. Therefore, a $5 bet on Fortune leads to an expected loss of 39.14 cents, minus 5.34 cents for every extra player involved. The table below outlines the break-even points for making versus not making the Fortune bet based on the total number of players.

• 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 instance, if there are four participants total (including yourself), it would be advantageous to place a Fortune bet if your initial pai gow poker wager is $17 or higher, but you should avoid it if it's $16 or lower.

Based on my understanding of tennis rules, a player wins a set by being the first to win six games with a minimum margin of two games. If both reach six games, a single tiebreak game is played. The table below details the statistics on winning a set based on the likelihood of winning a given 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 calculating the probability of winning a game, denoted as 'p', and losing, denoted as 'q', can be summarized as 1*p.⁶ + 6*p⁶*q + 21*p⁶*q² + 56*p⁶*q³ + 126*p⁶*q⁴ + 252*p⁷*q⁵ + 504*p⁷*q⁶

I appreciate your encouragement. I've only received a handful of personal queries, four to be exact, in my first 134 articles. However, since August 2005, the number has surged, largely due to my webmaster, Michael Bluejay who managed to rank us first on Google for searches like 'Is my boyfriend cheating on me.' We're now in second place. To your point, yes, there is a link here. I analyze both casino games and life with a deliberate perspective, and when offering advice in either realm, my aim is to suggest what might lead to the querent's greater happiness in the future.

Casino Royale stands out, providing an impressive 100x odds. For an in-depth overview of gaming conditions in Las Vegas, please check my recent update. Vegas craps directory.

Absolutely. If the commission is assessed only on winnings, it should indeed apply to the initial bet amount rather than the winnings themselves.

Now is not the ideal time to allow a minor issue to become a significant problem. The evidence regarding his connection to this other girl is rather weak. If you hope for him to be there for you and the baby, try to be more kind and understanding. Constantly questioning him about an address in his wallet might only push him further away, potentially even back to Puerto Rico.

My webmaster, Michael Bluejay, shares your enthusiasm for the quirky places. He never misses the chance to visit the Western, lamenting its transformation with, 'That place has really improved.' Unlike the other budget casinos downtown, like El Cortez and Gold Spike, the Western has a notably cleaner environment regarding smoke. Closer to your friends, I highly recommend the Rainbow Club and El Dorado in downtown Henderson, both of which are charming old-school spots catering to local low-rollers. However, both are certainly a step up from the Western. Here's Michael's take on skanky Vegas hotels .

In reality, all gambling winnings are taxable. However, players at table games typically operate on an honor system. A W2G form is generated if someone wins $600 or more, provided the odds were 300 to 1 or greater. Usually, this comes into play with progressive jackpots. Additionally, if a cash transaction exceeds $10,000, the casino must complete a Cash Transaction Report (CTR). Still, there's no need for concern; many high-stakes gamblers often worry unnecessarily about these matters.

This situation often arises when relationships move too quickly. Genuine connections take time to develop. In the future, pace yourself and refrain from diving into love until you truly know the other person well. An iPod, even if filled with romantic tracks, will only get you so far. I suggest you consider a cooling-off period of a month or two where you both take time apart. Afterward, if you both agree, you can reconnect with a more patient approach.

Several readers asked for a more detailed explanation. Solving this requires some basic matrix algebra.

Begin by letting 'x' represent the solution, or the average number of flips needed until there’s a difference of three between heads and tails.

Define 'y' as the expected number of flips when one side is leading by a single flip.

Designate 'z' as the expected number of flips when one side is two flips ahead in the game.

Post the initial flip, one side will be ahead by a single flip, making the equation x=1+y.

When either side leads by one flip, the next flip could either revert to a tie or increase the lead to two flips, both scenarios being equally likely. Hence, y=1+0.5*x + 0.5*z.

When one side is ahead by two flips, the next flip might bring the score back to just one flip ahead or conclude the game entirely, making both outcomes equally probable. Therefore, z=1+0.5*y.

Now we have three equations with three unknowns:

(1) X= 1+y

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

(3) Z = 1+ 0.5y

To solve these equations, let’s first eliminate the decimals by multiplying the last two by two.

(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

Now substitute y = 8 in (1) to get

(6) x = 9

Physics isn’t my area of expertise, so I consulted two physics authorities, my father and Andrew N. Both concurred that a ball can travel farther in high humidity compared to low humidity, and Andrew N. explained the fundamentals.

This is an intriguing inquiry. After researching online, it seems that a ball does indeed travel further on humid days compared to dry ones, assuming all other factors remain the same. The two key components are: 1) air density and 2) air viscosity.

1) Air Density

Interestingly, contrary to common assumptions, humid air is actually less dense than dry air. Water molecules occupy the same volume but weigh less than the combined oxygen and nitrogen molecules. This lighter air results in reduced buoyancy for the football since it displaces less mass. That said, the density of dry air at 20°C and 700 kPa is approximately 8.33 kg/m³, while the same atmosphere with 42.1% relative humidity comes to about 8.32 kg/m³, a minimal difference of roughly one-tenth of one percent. Thus, it seems unlikely this variation would significantly affect the distance achievable.

(*) - 700 kPa is elevated pressure, though it’s the best data I could locate. Nonetheless, in mechanical terms, it closely resembles normal pressure, which suggests that the details I’ve referenced should apply under typical atmospheric conditions (101.325 kPa).

2) Air viscosity

Viscosity plays a crucial role in influencing the drag force experienced by a football. When the viscosity is lower, the drag force is also reduced, which can lead to a longer distance traveled by the ball. For instance, in conditions of dry air at a temperature of 20°C and a pressure of 700 kPa, the dynamic viscosity is measured at 18.3 Pa*s. In contrast, when the air contains 42.1% humidity, the viscosity drops slightly to 17.8 Pa*s. This difference is about 3%, which may seem minor, yet it is more noteworthy than the impact of air density. Additionally, it is important to note that despite the small change, humid air still facilitates a longer trajectory for the football.

To verify this concept with practical evidence, I came across a resource golf website that provides insights into the flight distances of golf balls under both dry and humid conditions:

The findings clearly indicate that golf balls tend to travel farther in humid air, but the increase is typically just a yard or two at most. Thus, while humidity does encourage a longer flight for projectiles like golf balls and footballs, the effect remains fairly minimal.

Andrew N

Data culled from:

wipos.p.lodz.pl/HighTech/example1/ (which contains data on humid environments at 20°C and 700 kPa). The link is functional.
physics.holsoft.nl/physics/ocmain.htm (offering tools for calculating properties of humid air. This link is operational.)

Comments from the Wizard: To elaborate on the previous point, Boyle’s Law indicates that at the same temperature, the volume of a gas inversely changes with pressure. Therefore, when both temperature and pressure are kept constant, the gas volume remains unchanged, meaning the number of molecules per unit area stays the same. The atomic weights of gases are that oxygen is 16, nitrogen is 14, and hydrogen is 2. Consequently, a water molecule (H2O) has an atomic weight of 18, which is lighter compared to the heavier O2 and N2 molecules which weigh 32 and 28 respectively. This means that in humid conditions, the lighter water molecules can effectively displace the heavier oxygen and nitrogen molecules, resulting in lower air resistance for the football as it moves through the atmosphere. atomic weight This encompasses mathematically accurate strategies and insights applicable to casino games such as blackjack, craps, roulette, and many more that are available to play.