Ask The Wizard #134

The number of ways you can choose 3 cards out of the 40 non-face cards is (40*39*38)/(1*2*3) = 9880. The number of ways you can choose 3 cards out of 52 is (52*51*50)/(1*2*3) = 22100. So the probability of not getting a face card is 9880/22100 = 44.71%. Thus the probability of getting a face is 55.29%. His side of the bet had a 10.58% advantage.

From my pai gow poker section we have the following probabilities.

Player wins both 28.61%
Tie 41.48%
Banker wins both 29.91%

So you are getting away with a 4% commission. As player your expected value is .2861*0.96 - .2991 = -2.44%. As banker (going one on one) is .2991*0.96 - .2861 = 0.001036. So a 4% commission lowers the house edge by about 0.3%.

P.S. In May, 2008, a reader wrote to say that the Borgata does use quarters in pai gow poker, and forces bets to be in increments of $5.

I believe the policy at most casinos is that for large transactions you can have the funds any way you want. Before you consider laundering money by turning cash into checks be aware that casinos ask for a Social Security number and make a record of any transaction involving $10,000 or more.

Here is the probability of winning zero per game according to the number of plays.

The table is based on a random simulation. I know it is theoretically possible to get a win of zero in 100-play, but in 15,820,000 games it just never happened. So please don’t write about that. The table shows the probability of getting zero in 10-play is 0.025914, or 2.59%. The probability of this happening ten times in a row is 0.025914¹⁰ = 1 in 7,323,073,295,177,980.

I tried the software in question in free-play mode and my results seemed fine. In particular in 10 games I won something every time. However as far as I know no casino offers this software and takes real money players from the U.S. I’ll plan to do some further investigating but don’t want to explain how in this forum.

No splitting costs the player 0.58%.
No doubling costs the player 1.47%.
No splitting nor doubling costs the player 1.91%.

Here are the probabilities:

3 dice: 25.93%
4 dice: 48.77%
5 dice: 66.13%.

Yes. Any video representation of a card game in the state of Nevada must be dealt from a fairly shuffled deck. In other words you should expect the same kind of outcome as in a live game with the same rules. So basic strategy tables will also work for video blackjack.

[Bluejay adds: Every video blackjack game I’ve seen pays only even money on naturals, which significantly increases the house edge.]

No! The probability of winning is 15/36 = 41.67%, for a house edge of 16.67%. Even if the 2 and 12 both pay 2 to 1 on the field the house edge is only 5.56%. The over/under 7 bet ties for the any 7 bet as the worst bets on the table.

There are six ways to arrange two suits out of four for each pair. Then there are 44 cards for the singleton. So the number of successful combinations is 6*6*44 = 1584. There are 2,598,960 combinations in total, so the probability is 0.0609%.

Here in Vegas, yes you can.

A strategy of going for a royal at all costs, as if all the other hands paid zero, would result in a return of 47.85% on a 9/6 Jacks or Better game. The expected frequency of a royal would increase from once every 40388 hands to once every 23081.

Not often. Contrary to popular myth the casinos don’t tighten the machines on weekends or whenever it is busy. Here in Las Vegas the casinos have to fill out a form every time they change the percentage on each game. Most slot managers I have spoken with have a policy on what coinage is set to what return. I tend to think the most likely reason to change the percentage would a change in ownership and/or management, which do not happen often.