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# Ask the Wizard #146

Thank your for your informative column. I have been using the "Fun" mode to practice the basic blackjack strategy online (Golden Palace and Grand Online Casino). I generally do well on the fun mode, but when I go to "Real Money" mode I start losing quickly using the same strategy. Do the online casinos change the software randomness for "Fun" mode letting us win, only to entice us to deposit real money.

Mike from Prescott, Arizona

You’re welcome. It’s rare for online casinos to intentionally let players win in free mode. I know the Elka casinos used to do this (for which I blacklisted them), but fortunately they seem to have vanished. If anyone can show me hard evidence that a casino is intentionally allowing players to win in fun mode I would be happy to investigate it. Hard evidence means, at a bare minimum, a record of hands won and lost in each mode, for several dozen hands. Simply telling me that you lost "a lot more" when in real mode is useless.

I would like to play on line for free. Do the sites utilize your log in info to solicit? I want one that does not. I particularly like to play nine line Cleopatra but the online versions are not the same (that I have Found) What is the best no strings web site to play for fun?

Sue from The Colony, Texas

There are 3 dice, 2 are proper six sided dice, while one is a die with all sides containing a six. All the dice are in my pocket. I randomly take out a die and throw it. The result is a 6. What is the probability that the die was one of the proper dice with 6 different values?

Annojh from Toronto

Let A = Choosing the normal die
Let B = Rolling a 6 with randomly chosen die
Answer = Pr(A given B) = Pr(A and B)/pr(B) = ((2/3)*(1/6))/((2/3)*(1/6)+(1/3)*1) = (2/18)/((2/18)+(6/18)) = 1/4.

Thanks for the help your site has given. You’ve probably saved me thousands. I was playing in a NL Texas Hold 'em tournament on-line recently, and was dealt pocket kings (at a 10-man table) only to be dominated by pocket aces. I'd like to know the probability, given the condition that you have a pair, of at least one other player at the 10-man table having a higher pair than yours (in other words, having a "dominated pair"). Thanks again!

Dan from Cairo, Egypt

The following table shows estimated probabilities that a pair will be beaten by at least one higher pair according to the number of players (including yourself). These probabilities are not exact because the hands are not independent. However to find the exact probabilities would get complicated and I think these are pretty close. My formula is 1-(1-r*combin(4,2)/combin(50,2))(n-1), where r=number of higher ranks than your pair, and n = total number of players. The table shows the probability of another player having a pair of aces, when you have a pair of kings, in a 10-player game, to be 4.323%.

### Probability Pair Beaten by Higher Pair

Pair 2 Pl. 3 Pl. 4 Pl. 5 Pl. 6 Pl. 7 Pl. 8 Pl. 9 Pl. 10 Pl.
KK 0.49% 0.977% 1.462% 1.945% 2.425% 2.903% 3.379% 3.852% 4.323%
QQ 0.98% 1.95% 2.91% 3.861% 4.803% 5.735% 6.659% 7.573% 8.479%
JJ 1.469% 2.917% 4.344% 5.749% 7.134% 8.499% 9.843% 11.168% 12.473%
TT 1.959% 3.88% 5.763% 7.609% 9.42% 11.194% 12.934% 14.64% 16.312%
99 2.449% 4.838% 7.168% 9.442% 11.66% 13.823% 15.934% 17.992% 20.001%
88 2.939% 5.791% 8.56% 11.247% 13.855% 16.387% 18.844% 21.229% 23.544%
77 3.429% 6.74% 9.937% 13.025% 16.007% 18.887% 21.668% 24.353% 26.947%
66 3.918% 7.683% 11.301% 14.776% 18.115% 21.324% 24.407% 27.369% 30.215%
55 4.408% 8.622% 12.65% 16.501% 20.181% 23.7% 27.063% 30.279% 33.352%
44 4.898% 9.556% 13.986% 18.199% 22.205% 26.016% 29.64% 33.086% 36.363%
33 5.388% 10.485% 15.308% 19.871% 24.188% 28.273% 32.137% 35.794% 39.253%
22 5.878% 11.41% 16.617% 21.517% 26.13% 30.472% 34.559% 38.405% 42.025%

I have been researching Casino Bar because they have a nice bonus today. I ran across your claim that their software does the equivalent of "dealing seconds", but I see that your information was last updated about two years ago. I was wondering if you know of any change in that situation, please. I suspect you would have updated the page if there had been a change, but I thought I would ask. Where could I find a basic strategy sheet for a casino dealing seconds? (the bonus may or may not still be playable). Am I right in thinking the house edge is close to 5% in such a game? Of course, if that is the case I may as well play tricard poker. Thank you for a great website. Do you accept donations?

Ricardo from Malden, MA

When I find a casino is not playing fair I don't generally go back to check if they've stopped. Sometimes I do if requested by the casino and I feel the problem may have been accidental. Following is a basic strategy, based on infinite decks, where the dealer stands on soft 17 and deals seconds. What I mean by dealing seconds is that if the third card, and only the third card, would break the dealer it is skipped and the next card is played, whatever it is. Otherwise play continues normally. The house edge under this game would be 9.3%. I used to ask for donations but got so few I quit asking. Now the site is comfortably supported by advertising revenue anyway.

When playing video poker will it decrease my odds of winning if I put a \$50 bill in, instead of \$5 or \$10 increments?

Karen from Eastchester, New York

No. Neither the amount you put in nor the denomination affects the odds. The same is true of slots.

In the October issue of Casino Player magazine, Frank Scoblete wrote an article on controlled dice shooting where you state you lost \$1800 to Stanford Wong when he rolled only 74 sevens in 500 rolls. Why did you bet on such a small sample (500)? A person who claims to be able to control the dice should be willing to demonstrate their skill with a least 50,000 rolls. Am I wrong in thinking that 500 rolls is such a small sample that just about anything could happen?

Gerald from Alexandria

I lost the \$1800 to another gambling writer, not Stanford. I would have preferred more rolls but there was an obvious time contraint. Assuming one throw per minute it would take 34.7 days to throw the dice 50,000 times. I wasn’t the one who decided on 500 but it seemed like a reasonable compromise between a large sample size and time. You are right that 500 is too few to make a good case for or against influencing the dice, but 500 throws is better than zero.

If you can roll six dice only once, what is the probability of rolling 6,6,6,6,1, and 4 in any order?

Aubrey from Kokomo

There are 6!/(4!*1!*1!) = 30 ways to arrange these numbers in any order. Another way to look at it is there are 6 positions to put the 1, and 5 left to put the 4, so 6*5=30. The probability of getting 666614 in exactly that order is 1 in 66 = 1 in 46656. Multiply that by 30 for the 30 possible orders and the answer is 30/46656 = 0.0643%, or 1 in 1552.2.