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Ask the Wizard #130

Why do people gamble at all? Especially in a casino, where they know they are supposed to lose? Can you see this happening in any other business? What is the psychology behind this? Something for nothing? No, they do not keep what they win, most just lose more back later, that can’t be it. Socializing? No, you can do that in a restaurant, that can’t be it, and the list goes on. So what really is the problem? I work in a casino, and see it everyday, and almost the same people, everyday. In many cases they do not seem to be having any fun, that cannot be the goal. So, what, in your opinion, is it that is so addicting about losing money, and not using the sense you have been given?


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).

If you have 30 people, all born in the same 365-day calendar year, what is the probability that any two of them will have the same birthday? Please explain the formula in your response.

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%.

I’m a croupier working in a UK casino and just thought I’d point out that our version of Three Card Poker has a slightly different paytable than any of the ones listed on your page.. We pay 35-1 for a straight flush, and 33-1 for three of a kind (then 6-1, 4-1 and 1-1 for the other 3).

Richard T.

The house edge of that pay table is 2.70%.

How many eggs do you start with if each day you sell 1/2 the eggs plus 1/2 an egg; after 3 days you have zero eggs? At the end of each day, the number of eggs is a whole number.


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.

In a single-deck game, what is the probability of getting at least one ace and deuce in four cards? This is useful to know for the game of Omaha.


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.

Due to table-game tips to dealers being "highly recommended", each hand/play costs or "loses" the player a little bit (as little as ~$0.50-$1.00 just to be considered ’live’ by dealers) each time. With games of low bankrolls and minimum bids (i.e. ~$1000 in pocket and ~$2 per play), the tip & house-edge would often make games like video-poker more worth while as far as returns and (possibly) comps are concerned.


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.]

What is the standard deviation on the Ante & Play bets in Three Card Poker?



I'd like to how much does a casino poker chips weigh, and better yet do you know where is the best place you can purchase poker chips that feel and sound (when you drop them) are as close to the real deal as possible?


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.

What are the odds of being dealt the jack of diamonds 27 hands in a row in a six-card game?


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.