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The value of the consolation prize per card is 50/n, where n is the number of competing cards. For example, if there were 1000 competing cards, then the value of the consolation prize per card would be 5 cents.
On your video poker double double bonus poker strategy page, you state that if your are dealt 5 6 7 8 9 , that it is correct to hold the straight. It just seems counter-intuitive to me, but if you could explain in a little more detail about why going for the straight flush is poor strategy, I would be grateful.
— David from Montego Bay
In double double bonus a straight flush pays 50, a flush pays 6, and a straight pays 4. The probability of making the straight flush is 2/47, of a flush is 7/47, and of a straight is 5/47. So, the expected return of discarding the 9
is (2/47)×50 + (7/47)×6 + (5/47)×4 = 3.4468. The expected return of the straight at 4 is much more.
What happened to the card game 3-5-7 in Las Vegas? I cannot find it anywhere.
— Vince from North Collins, NY
I'm told that game had to be pulled out of the U.S. casinos, because the game of patent infringement. According to the fourth quarter 2008 Statistical Report of the Nevada Gaming Control Board, the following are the table game counts in Clark County.
Unfortunately, they don’t say what the 243 “other” games are, so this isn't of much help to answer your question, but it is still worth mentioning.
Dear sir, I "clocked" an automated single-zero roulette game for 8672 games. My predetermined number came up an amazing 278 times. I chose the number because of the wear and tear of the pocket. How sure am I that this number has higher probability than 1/37?
— Marc from Rotterdam, Netherlands
If my terminology is correct, "clocking a wheel" means to predict where the ball will land judging by the ball speed, ball location, and wheel speed. It sounds like what you are doing is exploiting a biased wheel, which is a different advantage play. As long as we're on the topic, a third advantage play is exploiting "dealer signature," where the croupier is so consistent that the ball and wheel speed are nearly the same every spin. This allows the player to predict where the ball will land based on ball location and past results.
To answer your question, the expected number of times you should have hit your number is 8672/37=234.38. The variance is 8672×(1/37)×(36/37)=228.04. The standard deviation is the square root of the variance, or 15.10. You had 278-234.38=43.62 more hits than expected. That is (43.62-0.5)/15.10 = 2.8556 standard deviations. The reason for subtracting 0.5 is hard to explain. Suffice it to say it is an adjustment factor for using a continuous function to estimate a discrete function. Doing a Gaussian approximation, the probability of hitting your number that many times, or more, is 0.21%. So, there is a good chance you found a biased wheel. However, there is still a 1 in 466 chance it was just good luck.
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