Ask The Wizard #170

When employing an optimal strategy in a 9/6 Jacks or Better game, you can expect to draw a royal flush approximately once every 40,601 hands. Conversely, hitting four cards towards a royal happens once in about 460 hands. On average, you'll find yourself just one card away from a royal 88.33 times for every one you achieve. Out of the hands where you have four to a royal, 50.37% return nothing, 24.89% yield a pair, 7.89% result in a straight, 16.16% result in a flush, and 0.69% lead to a straight flush. Here are the precise statistics.

Based on the expected data, for 170 instances of having four cards towards a royal flush, you would anticipate approximately 1.92 royal flushes. The likelihood of not hitting any royals while expecting 1.92 is represented by 'e'.^-1.92= 14.59%.

For the initial wager, my calculation called for a pass line bet of around $90.91, though I rounded this to $100. A point was rolled—likely a 6 or 8. Unfortunately, on the shooter’s second roll, a seven was drawn, resulting in the total loss of our initial bet in just two rolls. This did not seem entertaining enough for television, and the story ultimately never aired.

I can foresee two questions that might arise: (1) Why did I have them bet on the pass line instead of the don’t pass? (2) Why didn’t I recommend betting $91 on the line and then $910 on the odds, covering the extra dollar myself? To address the first question, I believed the pass line provided a better chance for a rapid win. Although the don’t pass wager has a lower house edge, I felt it would take a longer time to reach the $5,000 target, thereby exposing more money to the house's advantage. To the second question, the distinction between 9x and 10x odds isn't significant, and I thought it would present better on camera to maintain a visual of black chips, at least at the beginning.

I have referenced your website to debunk myths and betting systems to many friends, and your data always proves to be effective. In the Pink Panther slot (and several others), there’s a bonus round featuring a grid with various images to choose from. Behind some images are cash rewards, while others reveal a symbol that ends the bonus round. Once the bonus board is displayed, the arrangement of the symbols remains fixed, correct?

That being said, it's my understanding that in all types of electronic games—including video slots, video poker, and video keno—the outcome is generally determined at the instant you make your selection. The combinations of possible results are continuously shuffled at a staggering rate, thousands of times every second. While I can't assert this about every slot machine, I believe with major U.S. slot manufacturers the outcome hinges on the precise microsecond you press the button to place your bet.

Last night, I found myself playing a casual game of poker with relatives. I turned to my husband and asked, 'Do you have a nine?' Suddenly, the hostess rebuked me, claiming I was soliciting hand advice. I insisted that was not my intention; I was merely engaging in table chatter. Although everyone seemed to side with her, I suspect it was just because it was my husband involved. Is there an official rule against soliciting hand information or directly inquiring what someone holds? I always thought players could freely express anything at the table, barring rules against inappropriate language. Please clarify.

I'm evaluating whether to replace my aging refrigerator now to save on energy costs, or to wait until it breaks down entirely. I can easily ascertain that the new fridge would be about $37 cheaper to operate each year compared to the old one. However, how do I account for the purchase cost of the new fridge? Let’s say the new unit retails for $425. I can’t simply classify the whole cost as a new expense because I’ll need to replace the old fridge eventually—if not now, then in the future. Assuming a typical refrigerator lifespan of 14 years, with my current unit being 9 years old, if I replaced it now, I’d need another replacement in 5 years. I tried organizing a table comparing costs over 9 years for keeping the current fridge versus buying a new one now, but it proved challenging to create a fair comparison because I wasn’t sure how far out to consider the costs, especially since the replacements would occur in different timeframes. How can I analyze the financial implications of replacing now versus later? Just to clarify, this isn’t my personal dilemma—my existing refrigerator is probably 30 years old. It's actually for a friend.

This isn't a question, merely a heartfelt thank you. Please continue spreading the message that there's no magical winning system. I retired at 51 years old and have managed to earn an average of $86K each year for the last 11 years playing craps. I genuinely want others to understand that winning consistently is unrealistic. Keep up the excellent work!

Fantastic site. I'm asking out of personal curiosity. In a four-player Texas hold’em game, I received pocket aces and subsequently completed a royal flush on the river. I’m curious about the odds of making a royal flush on the river when starting with aces.

The website www.ccc-casino.com features a version of roulette termed Super Chance Roulette that lacks a zero. With no zero present, are there any betting systems that could prove effective, and might one consider wagering on both black and red concurrently without the risk involved with the zero? combin I attempted to access that game but the site was down at the time of my visit. Nevertheless, assuming such a game exists, the answer remains no; no betting system could be expected to deliver a favorable outcome over the long haul. The expected value of all systems would consistently equal zero.

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