Ask The Wizard #177

I must confess that my 0.17% figure was an error. I discovered the flaw in my analysis when I recently updated it for the Microgaming rules. To all those who played it because of my 0.17% figure, I apologize.

It depends on the particular rules, but it is usually high because of a common rule that blackjack pays only even money. I checked at the Suncoast and they have the following rules: one deck, dealer stands on soft 17, blackjack pays even money, late surrender allowed, player may only double on 10 or 11, double after split not allowed, split aces get one card each, only one split allowed, six card Charlie, dealer must stop with six cards. The house edge of this game is 2.39%.

If the probability of something is p then on average it will take 1/p trials for it to happen the first time. Obviously, on the first roll you’ll cross off one number. The probability of rolling one of the other five numbers next is 5/6. So it will take on average 1/(5/6)=6/5=1.2 rolls for that to happen. Following that reasoning to the end, the expected number of rolls is (6/6)+(6/5)+(6/4)+(6/3)+(6/2)+(6/1) = 14.7.

It doesn’t make any difference what the past spins were. The probability of red 23 three times in a row is (1/38)³ = 1 in 1 in 54,872.

Assuming the player followed the strategy for the conventional Las Vegas rules, where the player wins the ante on a straight or higher, the house edge would go up from 2.04% to 3.51%. This I’m sure could be lowered with rule specific strategy changes. However, it takes my computer 71 days to analyze this game so please forgive me if I end my answer here.

First, it is important to remember that the U.S. only accounts for half the market. Outside of the United States I think the industry will become more legitimate as the United Kingdom takes a greater role. However, as publicly traded companies, most of the U.K. operations out of respect for U.S. laws no longer accept American players. This will leave American players with a greater percentage of less reputable organizations to choose from (Bodog excepted of course). So, the short-term effect will be that American players are less protected and more likely to be cheated. In the long term, hopefully we will come to our senses and learn all over again that prohibition doesn’t work and repeal this stupid law. This will likely take several years.

According to my interpretation, this law does not make gambling online illegal. The bill seeks to choke off Internet gambling by making it illegal for U.S. banks to directly fund casino accounts. However, they stopped accepting credit card transactions years ago. This law only addresses what nobody was doing anyway. Any business outside of the United States is not obligated to respect our laws in their own country. Some are choosing to anyway, some are not. If your Internet casino of choice is still accepting U.S. players, I suggest you be honest about where you live and continue to use whatever method of payment you were using before. Personally, I find Neteller to be the most convenient.

I hope you’re happy, I just added a new section answering questions such as this for 1 to 25 dice. As the five-dice table shows, the probability of rolling a total of 12 is 0.039223251028807.

Regardless of what the first number is, the probability the second spin only matches it is (1/37)*(36/37). The probability only the third spin matches it is (36/37)*(1/37). The probability neither spin matches, but the second and third match each other, is (36/37)*(1/37). The probability both second and third spins match it is (1/37)*(1/37). Add up all this and you get 3*(1/37)*(36/37)+ (1/37)*(1/37) = 7.962%.

I asked this question of “Brain”, a casino manager. Here is what he said.

Table minimums are basically the price point at which we can "sell" the games. These fluctuate based on the clientele in-house, hotel occupancy, individual customer needs, etc. We use a 10X multiple for our maximum to protect us from large betting swings or counters.

We will get complaints from guests such as: Why don’t you lower this blackjack table to a $5 minimum? They don’t understand that one $10 player is worth more to the casino than two $5 players. Or that one $25 player is worth more than three $10 players.

Most casinos monitor capacity by counting the number of players periodically (e.g., every hour) and comparing it to the number of spots available. This is tricky because there is an actual capacity (total number of spots on a table) and what I consider a comfortable capacity, which is how many people can comfortably sit at a table. Unless there are no options available, most people prefer to play at a table with one or two open spots so they have room to stretch out and aren’t rubbing elbows.

Based on capacity, at any time during the evening we may lower or raise our table limits.

My personal philosophy is to have lower limit tables near the entrances and high traffic areas to give the appearance that we are busier. I rarely raise a minimum on a table in play, but may lower it. If I do raise a minimum, I always "grandfather" the seated players in.

Brian didn’t get into the ratio of the maximum to the minimum bet but a similar question was asked before. I asked an executive with a major Las Vegas casino about it at the time and he said they like to corral their big bettors into the high limit areas.