Ask The Wizard #166

I have begun playing 3-card guts online for play money (they do offer live games), my question is.... Where can I find a guide for what would be a medium starting hand in a 10 handed game...9 handed..8 handed , and so on. The hand rankings are the same as three card poker. I have found the probabilities for three card poker on your site. But I do not know how to go deeper to find the medium expected hand. Can you help?

Annie from Prior Lake

Following is the median high hand according to the number of players. This is based on an assumption of independence between hands, which is not the case, but the table should still be a very close estimate.

Median Hand in Guts

Players Median Hand
1 K,10,2
2 A,Q,8
3 5,5,K
4 9,9,7
5 J,J,Q
6 K,K,5
7 A,A,7
8 8,5,3 flush
9 10,8,6 flush
10 J,10,6 flush

I lost a lot of money playing Cryptologic Blackjack today. While I don’t think anything is fixed, one aspect of my play seemed well outside the range of probability. Within 35 hands, the dealer showed a 6 seven times and won each time. This was verified through the logs. If the probability of a dealer bust is 56% with a six, my calculation suggests the odds of this independent event happening six consecutive times is 0.23%.

Adam from Toronto

At Cryptologic they use 8 decks and the dealer stands on a soft 17. According to my blackjack appendix 2, the probability of the dealer busting with a 6 up is 0.422922. So the probability of not busing is 1 - 0.422922 = 0.577078. The probability of not busing 7 times out of 7 is (0.577078)7 = 2.13%.

When counting cards, what seat has the best position to count cards on the table?

Nate from Marquette, MI

Mathematically speaking, third base is best because you have seen more cards by the time it is your turn, and thus have more information. However, given six positions at the table, I personally prefer the fourth position because I have a better view of the entire table.

In your last column you said that "The probability of 5500 coins not being a 55 can be very closely approximated as 0.9864012865500 = 1 in 507,033,772,284,213,000,000,000,000,000,000."

I assume "approximated" because of the effect of removal as you go through the 5500 coins. Talk about a minuscule effect of removal! This is a good example of the target coins becoming LESS likely as you remove non-targets, because the effect of removal is so small compared to the much larger probability of a crooked game, i.e. the target coins have been removed.

Pete from NY

Yes, I said “closely approximated” because there are only so many pennies in the world. Remove one non-55 from the bag and the effect of removal increases the probability that every other penny in the bag is a 55. If I hadn’t said “closely approximated” at least three people would have written in to correct me. It is of course an extremely minute effect, but many of my readers are perfectionists, and will jump all over me for the slightest of errors.

How does this work?

  1. Grab a calculator. (you won’t be able to do this one in your head)
  2. Key in the first three digits of your phone number (NOT THE AREA CODE)
  3. Multiply by 80
  4. Add 1
  5. Multiply by 250
  6. Add the last 4 digits of your phone number
  7. Add the last 4 digits of your phone number again.
  8. Subtract 250
  9. Divide number by 2

Do you recognize the answer?

Chris M. from Las Vegas

Let’s call the first three digits in your phone number x, and the last four y. Now let’s see what I have at each step.

  1. Ready!
  2. X
  3. 80x
  4. 80x+1
  5. 250*(80x+1) = 20000x+250
  6. 20000x+250+y
  7. 20000x+250+2y
  8. 20000x+250+2y-250 = 20000x+2y
  9. (20000x+2y)/2 = 10000x+y

So that is of course going to equal your phone number. We need the 10000x to move the prefix four places to the left, and then we add on the last four digits.

I was playing a triple-play deuces wild machine and was delighted to be dealt four deuces. I kept the deuces and discarded the queen and hit the draw button. Of course I was paid accordingly, but the stranger next to me freaked out saying that I should have held the queen instead of drawing a new card. He cited the fact that malfunctions void all payouts. In future situations, should I really be concerned about such malfunction possibilities?

Eric from Las Vegas

No. Malfunctions in any video based game are extremely rare. In slots with moving parts they are more likely, but still on the order of one in a million. In video poker, mid-play malfunctions are virtually unheard of. The reason usually given for holding all five cards with four deuces is that otherwise you might hold the wrong cards by pressing the buttons incorrectly. In my opinion the probability of this kind of human error is much greater than the probability of a malfunction.

I have a question about a blackjack tournament, where only the largest stack at the end is paid. Assume 1000 players start with 100$ in chips and can bet 5 hands at a time, from 1-10$ per hand. If no one knows anything about the other chipstacks, what chipstack should you be looking for before being satisfied?

Erin S from Rockford, MI

You didn’t say how many rounds there were. However, I would bet $10 in all five hands every hand, or go bust trying. With 1,000 players and a relatively low max bet you’ll need all the variance you can get.

Can you please explain to me how the table limits for roulette works and what is the difference between minimum limit for individual number and table. If possible, please give examples.


There are usually two minimums in roulette. For example: $5 outside, $1 inside. Outside bets are all even money bets, column bets, and dozen bets. Inside bets are those on the numbers, including groups of 2, 3, 4, 5, and 6. In this case the minimum on outside bets is $5 and $1 on inside bets. However, you must bet at least $5 in total on inside bets or make none at all.

Question: I am NOT a lawyer! But somehow I have the idea that online gambling violates some sort of legal statutes here in the states. If so, then are not people sort of publicly admitting to breaking the law when they state in emails,etc. to you or you yourself that I played online casino X and won/loss Y dollars. Of course the law is probably overwhelmed with REAL crime but if folks are going to admit in writing that they have broken the law then the law does not have to work hard to prove the fact. So it seems that folks should be careful about they tales of online gambling experiences in public forums. Seems like it would not take a whole lot of work by some DA to say look for all those folks in his jurisdiction with such admissions and charge them with whatever DA charge people with.


As far as I know the number of players to be prosecuted for gambling on the Internet is zero. So far efforts have been aimed at choking off the industry at the payment processing level, which has only moved those services outside the country as well. Laws directed at the player are simply not enforced. There are lots of poker celebrities who publicly earned seats at the big poker tournaments by playing poker online, and to the best of my knowledge, none of them have been prosecuted . However, Washington State recently made playing poker online a felony, so I might be nervous in the Evergreen State.

If everyone who gambled quit the second they were ahead, I believe there would be a few casinos in bankruptcy. Given that your bankroll will fluctuate a good bit, won’t most people be ahead at some point in their gambling (of course meaning the house is behind)?


I disagree, at least for the reason you state. Under your scenario most people would indeed leave Vegas winners. However, some players would lose the first bet and keep falling deeper and deeper in the hole after that, until they exhaust their entire bankroll. Assuming the same game and player strategy, the overall house edge would remain the same regardless of player money management strategy. In other words, betting systems not only can’t overcome the house edge, they can’t even put a dent in it. Getting back to your question, if everyone quit as soon as they were ahead, there would be a lot less gambling going on. So while the house edge would be the same, it would be applied to less total money bet, which would indeed hurt the casinos financially.

There are two tables in a room. On the one to the right there are a 100 coins, 20 with H facing up and the rest (80) with the T side facing up. There are no coins on the other table. The goal is to somehow move the coins so that there will be an equal number of coins with H facing up, on both tables. You cannot see the coins (dark room) or touch them to tell if they’re facing "up" or "down".

Dan from Tel Aviv

Go to my other site, for the solution (spoiler warning!)

With the continuing gains in popularity of slots/VP and new table games (3 card poker, let it ride, caribbean stud, etc.), have any (major) casinos stopped offering the "classic" table games (blackjack, roulette, craps, etc.)?

Dean M. from Toronto, Ontario

Interestingly, the Casino Royale here in Vegas has zero legitimate blackjack games. I believe they have four Blackjack Switch games and one 6 to 5 game. They still have craps and roulette.