Ask the Wizard #166
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
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%.
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.
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.
- Grab a calculator. (you won’t be able to do this one in your head)
- Key in the first three digits of your phone number (NOT THE AREA CODE)
- Multiply by 80
- Add 1
- Multiply by 250
- Add the last 4 digits of your phone number
- Add the last 4 digits of your phone number again.
- Subtract 250
- 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.
- 250*(80x+1) = 20000x+250
- 20000x+250+2y-250 = 20000x+2y
- (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.
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.
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.
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.
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.
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.
Dan from Tel Aviv
Go to my other site, mathproblems.info for the solution (spoiler warning!)
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.