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Ask the Wizard #130
People generally gamble either for entertainment or because it’s a compulsion, so let’s look at each.
I think those who like gambling find it exciting and a safe way to get an adrenaline rush, much like riding a roller coaster. For the knowledgeable gambler the entertainment can actually be cheap. Although gambling feels like a job to me now I played recreational basic strategy blackjack for about a year before I went onto card counting. Playing $5 a hand under Atlantic City rules at a full table the expected loss per hour is only 2 cents per hand or about $1.20 per hour. That isn’t much to pay for the entertainment and free drinks. So those who play the better games and play them well could certainly make an argument that it is a small price to pay for entertainment.
Some people, like you, don’t see what is entertaining about gambling at all. That makes sense, since not everyone likes every form of entertainment. Just because some people like baseball doesn’t mean everyone will.
As for compulsive gambling, psychologists say compulsive gamblers fall into two groups: those who do it to it for the action and those who do it to escape reality. The action seekers tend to be men and gravitate towards the table games. The escapists tend to be women and gravitate towards slots and video poker. So that is my two cents. Keep in mind the only psychology I have studied was one semester in high school, 20 years ago (hard to believe it has been that long).
Scott from Madison, Indiana
Think of the 30 people as lined up. The probability the second person doesn’t match the first person is 364/365. Then, assuming they didn’t match, the probability the next person does not match either of the first two is 363/365. Then keep going one person at a time. The overall probability no two people match is (364/365)*(363/365)*...*(346/365) = 29.3684%. It is often asked what is the fewest people you need for the probability of a match to be at least 50%. The answer is that with 23 people the probability of at least one match is 50.7297%.
The house edge of that pay table is 2.70%.
Let’s let d (for day) be the number of eggs at the beginning of the day and n (for night) be the number at the end. The problem tells us that d/2 - ? = n. So, let’s solve d in terms of n.
d/2 = n + ?
d= 2n + 1
So on the third day n=0, so d=1.
On the second day n=1, so d=3.
On the third day n=3, so d=7.
So there you have it, you started with 7 eggs.
From probability 101 we know Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B). So Pr(A and B) = Pr(A) + Pr(B) - Pr(A or B). Let's let A be getting an ace and B be getting a deuce. Pr(A) = Pr(at least one ace) = 1-Pr(no aces) = 1-combin(48,4)/combin(52,4) = 1-0.7187 = 0.2813. The probability of no deuces would obviously be the same. By the same logic pr(A or B) = Pr(at least one ace or deuce) = 1-Pr(no aces nor deuces) = 1-combin(44,4)/combin(52,4) = 1 - 0.501435 = 0.498565. So the probability of getting at least one ace and deuce is 0.2813 + 0.2813 - 0.498565 = 0.063962.
You make a good point. Tipping definitely does add to house advantage in table games. If one were to tip one bet until every 100 hands that would add 1% to the house edge. Slot and video poker players also get comped and in general treated much better. These are things to consider when deciding which game to devote your time to.
[Bluejay adds: When you consider tips, video poker can lose less per hour than table games but only slightly, while slot machines remain a money-sucker. Consider 99%-return $0.25 video poker at 500 hands an hour, which is $6.25/hr. in expected losses. This compares favorably to blackjack with an hourly loss is 0.5% edge x 100 hands x $5 = $2.50, + $5/hr. tips = $7.50/hr. A typical quarter slot machine loses more than twice that per hour.]
The standard is 11.5 grams. Casino-quality chips are made of a clay composite. Most poker chips sets are the same weight but the material is not as high quality and feels more like plastic. If you really want the best you could go to a casino and purchase a large quantity of $1 craps/poker chips from the cage at face value. If the casino changes the style, or goes the way of the dodo bird completely, the chips should go up in value. However for most recreational purposes there are always lots of sets available on eBay for about $50 for a 500-chip set. If you do get generic chips I would recommend true Paulson chips (there are many imitations), which are the same quality as casino chips. However Paulson no longer makes generic chips so the price will be significantly higher. If the price pushes $1 a chip, which it often does, I would just get actual casino chips instead.
The probability of getting it any one hand is 6/52. The probability of getting it 27 hands in a row is (6/52)27 = 1 in 20,989,713,842,161,800,000,000,000.