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Greetings, Mr. Wizard. I've been a visitor to your website for nearly a year now, and I want to express my gratitude. I appreciate not only the creation of the site but also your ongoing efforts to refresh it with valuable and insightful content. I can only imagine the hours you've dedicated to maintaining it.

I have several inquiries. First, let's discuss the banners. I'm curious about how we can enhance your revenue through banner clicks. Is your compensation based on the total number of clicks, unique visitors, a flat rate, or perhaps a different method? At the moment, I only click on new banners, but I'm willing to click on several each time I visit if it could contribute to your income.

Next, I would like to delve into your ideal approach for playing Jacks or Better and the associated practice game. I don't mean to sound naive, but my past questions haven't deterred me from seeking clarity. On a Jacks or Better table, how do you determine the ranking of a hand that has one high card (A, K, Q, J) but no penalty cards? Additionally, related to this, the practice game's suggestion is to hold the K and Q while discarding the A with the lower cards for a hand of unsuited A, Q, and K. Intuitively, I would think that keeping the Ace is a better strategy. What are the benefits of discarding the Ace, and how can I identify the best play in this scenario?

Denis from Rochester, New York

Thank you, Denis, for your thoughtful remarks and your willingness to support the financial stability of this site. When you first contacted me, just clicking my banners was beneficial. However, as I update this in 2013, it's more about acquiring new users that sustains me. Clicking the banners isn't very effective if users don't create an account and ideally deposit funds.

You can see from my 9-6 jacks or better strategy There exists a singular line for 'one high card' because the worth of an individual Jack to Ace is fairly uniform.

Could you please direct me to where I can find a print-friendly version of blackjack odds to keep in my purse? I'm just beginning to learn the game, and I'm uncertain when I should hit or stand.

Sue from Marquette, USA

A suggestion would be to right-click on any of my strategy charts, save the image, and print it out. Some stores in casino gift shops offer basic strategy charts that are the size of a business card, but keep in mind these often contain at least one error about half of the time.

This website is quite fascinating; do you earn your income as a gambler? Have you explored the probabilities related to stock index futures trading?

Randy from Aurora, Illinois

I'm curious about futures trading, but time constraints are preventing me from diving into it right now. My earnings are derived from advertising revenue on this site (please support by clicking the banners) and consulting fees for analyzing new casino games.

Fantastic website! Is there a way to download your pai gow practice software so that I’m not always required to play online? Thank you in advance.

Abraham from Ocean, New Jersey

Sorry, there isn't.

Are the probability statistics for craps, including the odds, entirely accurate? Also, is the gaming industry your main profession, and do you often visit Atlantic City? Furthermore, how do you simulate billions of hands, spins, and rolls? Is it done via computer software, and if so, which one?

DB from New York, USA

Mistakes can happen to anyone, but craps lends itself to mathematical analysis, so I am quite confident in my odds for the game. Yes, my full-time work is self-employed in some form of gambling. I’ve visited Atlantic City many times in recent years, but two months ago, I relocated to Las Vegas, so I fear I won’t be seen in Atlantic City frequently anymore. I prefer combinatorial methods over random simulations whenever possible. Regardless, I use my software created with Visual C++ for simulations, utilizing a Mersenne Twister .

The Stratosphere advertisement for poker machines that offer payouts exceeding 100%. In a previous article, you noted that a perfect strategy player can expect to hit a royal flush approximately every 40,388 games. Given this information, does this mean a player must engage in that many perfect hands before realizing the advertised payout percentage? I'm speaking on behalf of countless video poker enthusiasts who, like me, witness their $20 diminish to $0 in a '98%' machine. Jacks or Better No, that is a misconception. Contrary to what many believe, there is no cycle in these games. Each hand is random and independent. To truly ensure reaching the theoretical return of 99.54%, one would require an infinite number of perfectly executed hands.

Derek G from Vegas, baby!

Let me provide some statistics for you. Royals contribute 1.98% to the return in a 9-6 Jacks or Better game. Consequently, you can anticipate the game to yield 97.56% between royal flushes. The standard deviation for one hand is 4.42, while the standard deviation for the return over 40,391 hands, which is the average interval between royals, stands at 2.20%. Therefore, even after completing a full cycle for royals, you might still be far from achieving a 99.54% return. There’s a 95% probability that your returns will be somewhere between 95.24% and 103.85%.

Regarding pop-ups, I'm not fond of them either. However, they help cover necessary expenses. Think of them as the price you pay for the valuable information provided.

Hello! Do you sell or recommend a basic strategy card for blackjack? In the past, I’ve bought some from Winning Publishing NV. Your website is quite impressive.

The timing of your inquiry is perfect. Marsha Ness from Custom Strategy Charts is now selling laminated strategy cards for blackjack and Spanish 21. The strategies are crafted directly from my insights, and there is a broad selection based on various rules. However, at present, electronic payment options are unavailable, so you will need to send a check via postal mail.

Tom from Lancaster, USA

Update: Since you inquired, the Custom Strategy Cards business has now ceased operations.

I thought you placed the Golden Palace Casino on your blacklist, yet I just received an email promoting them from you. What’s the story behind that?

You're not the only one raising questions about this. My advertising partner believed my past issues with them were resolved and accepted their ad. I was not pleased with this and apologize for the situation. I hope this will not reoccur.

Grey from Singapore

No, I have considered it, but I fear that ordering a large quantity would leave me stuck with unsold inventory.

Do you sell t-shirts?

Dennis

I recently came across your website, and I must say it’s excellent. I noticed that online casino reviews have been removed; do you plan to bring them back?

I'm not entirely certain. The site has been underperforming in terms of advertising income, and I suspect viewers were skipping the ads to access the free links in the reviews. Essentially, I was directing too much free traffic.

Floyd from Mattoon, Illinois

Where can I find neatly printed and laminated credit card-sized versions of your basic strategy tables for blackjack? If you don’t have them, could you consider offering them?

I’m happy you asked! You can acquire them from Custom Strategy Cards, which feature my blackjack and video poker strategies on convenient, wallet-sized laminated cards.

Steve from Tucson, U.S.A.

Update from November 13, 2007: The Custom Strategy Cards website is now out of service.

I noticed that your online column hasn’t been updated since June. Are you alright? I hope everything is fine. I possess a basic strategy card for blackjack that has proven very helpful. Are there similar strategy cards for electronic poker games? Thank you for your time.

I'm uncertain regarding the specific online column you're mentioning. However, I’m doing well. In fact, you can obtain my video poker strategies in a practical strategy card format from Custom Strategy Cards. They might not be listed yet, but the owner does have them, so feel free to ask.

Charlie from Schaumburg, Illinois

Update: The Custom Strategy Cards company has unfortunately closed down.

Well done, great job! I have a question: I see in your May 5, 2003, column that you actually CALCULATE your blackjack odds. I find it intriguing that you aren't using a computer to SIMULATE the outcomes. Or is this a silly question, insinuating that it would take the computer a million years to complete the task?

Indeed, I calculate the odds for blackjack using a combinatorial strategy, analyzing all possible combinations of player and dealer cards to identify the highest expected value at each decision point. This method is more complex to program than simulations, but I find it more refined and a rewarding challenge in recursion. However, I have great respect for those who use simulations, as modern computers can efficiently handle a billion bets, closely approximating optimal strategy returns.

anonymous

I'm quite fond of your site. This morning, I was perusing your

and reflecting on your experiences with them— it seemed like you consistently lost everything you deposited. This was disheartening to read. When I noticed your request for donations, it became clear why you might be doing this! reviews of online casinos Explore the Top Online Casinos Available in Your Region

anonymous

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Greetings Mr. Wizard. I've been a frequent visitor to your website for nearly a year, and I'd like to express my appreciation. Thank you for not just creating this platform but also for regularly refreshing its content with valuable and enlightening information. It must take a significant amount of time and effort on your part.

anonymous

I have a few inquiries. First off, regarding the banners on your site, could you explain how clicking on them contributes to your earnings? Are you compensated based on the total clicks, unique visitors, a fixed payment, or some other criteria? Currently, I only click on banners that showcase something new, but I would be willing to click on several during each visit if that could boost your income.

My next set of questions pertains to your ideal strategy for the Jacks or Better table as well as the practice Jacks or Better game. I apologize if I seem uninformed, but I feel compelled to ask. When reviewing the table, where can I identify the ranking of a hand that includes only one high card (A, K, Q, J) and no penalty cards? Additionally, regarding the practice game, it suggests that for a hand containing unsuited A, Q, K with no penalties, the best move is to hold K and Q while discarding A. Personally, I would have expected holding the Ace to be the superior choice. Could you clarify the benefits of discarding the Ace and how I should assess the best move for this hand based on the table?

anonymous

Thank you, Denis, for your encouraging remarks and your willingness to assist in maintaining the financial viability of the website. In your initial message, you indicated that simply clicking on my banners was helpful. However, as I update this response in 2013, it has become clear that acquiring new players is what truly supports me. Clicking on a banner alone isn't particularly beneficial unless they create an account, ideally with a deposit.

Indeed, there exists a singular entry for hands categorized as having 'one high card.' This is due to the fact that a specific jack through ace is valued similarly.

R.S. from Dallas

Could you let me know where I might find a printable version of the odds for blackjack that I could keep in my wallet? I'm still in the learning process and unclear about when to hit or stand.

One suggestion would be to right-click on one of my strategy charts, save the file, and print it out. Some casino gift shops offer basic strategy charts the size of a credit card, but be aware that these charts may contain mistakes about 50% of the time. Texas Hold’em page ? Is that number significant?

anonymous

Your site is quite intriguing; do you derive your income through gambling? Have you analyzed the probability aspects of stock index futures trading?

While I am considering learning about futures trading, my current time constraints prevent me from delving into it. My earnings primarily come from advertisement revenues on this site (please consider clicking on the banners) and from consulting on the analysis of novel casino games.

anonymous

Fantastic website! Is there a way for me to download your pai gow practice software so I won't always need to play online? Thank you in advance.

Are the probability statistics for craps, including the odds, reliable? Is your work in the gaming industry your full-time job, and how often do you travel to Atlantic City? Furthermore, how do you simulate such huge numbers of hands, spins, and rolls? Is it done via computer software?

anonymous

Anyone can occasionally make errors, but craps is relatively straightforward to analyze mathematically, so I feel confident that my odds are accurate. Yes, gambling in various forms is my full-time self-employed occupation. I've frequented Atlantic City many times in recent years, but two months ago, I relocated to Las Vegas. Consequently, I won't be visiting Atlantic City as much from now on. I prefer a combinatorial analysis rather than random simulations when feasible. I develop my own software using Visual C++, and for generating random numbers, I apply a specific method.

You mentioned poker machines that boast payouts exceeding 100%. In a past article, it was indicated that a player employing the optimal strategy would average one royal flush every 40,388 attempts. Does this suggest that a player must hit this many hands perfectly to achieve the advertised return percentage? I'm speaking for the countless video poker enthusiasts who, like myself, have witnessed a $20 bankroll dwindling to nothing on that '98%' machine.

No, that is a common misconception. In reality, each hand is independent of the last. It would require playing an infinite number of hands perfectly to ensure reaching the theoretical return of 99.54%.

To break it down, royal flushes contribute 1.98% to the return rate in a 9/6 Jacks or Better game. This means one can expect an overall return of 97.56% between royal flushes. The standard deviation for an individual hand is 4.42, whereas after 40,391 hands—the average number between royals—the standard deviation of return drops to 2.20%. Therefore, even after achieving a complete royal cycle, it is entirely possible to fall short of a 99.54% return. Statistically, there’s a 95% chance that you will land somewhere between 95.24% and 103.85%.

anonymous

Regarding the pop-up ads, I share your dislike for them; however, they are necessary for maintaining my livelihood. Think of them as the price you pay for the valuable information you receive.

Hello. Do you offer or recommend a basic strategy card for blackjack? I previously purchased some from Winning Publishing NV, and I find your site to be excellent.

Ricardo from Malden, MA

Your inquiry comes at a timely moment. Marsha Ness, who runs Custom Strategy Charts, is currently in the process of selling laminated strategy cards for blackjack and Spanish 21. These strategies are directly from me and cover a broad range of rules. As of this moment, electronic payment options haven’t been established yet, so you would need to send a check by mail.

Update: Since the time of this question, the Custom Strategy Cards business has unfortunately ceased to exist.

Hector from Cardiff, UK

I was under the impression that you had blacklisted the Golden Palace Casino, yet I just received an email promoting their site. Can you explain? video poker appendix 1 You’re not the only one raising concerns. My advertising associate believed my ongoing dispute with them was resolved and accepted their advertisement. I was quite displeased and apologize for this oversight. I hope it won’t happen again.

No, I have considered it, but I'm worried that if I purchased a large quantity, I might end up with most of them unsold.

Edward from Placentia

I just recently discovered your site, and I think it’s great. However, I noticed the online casino reviews have been removed. Will they ever come back?

I'm unsure. The site's performance in terms of advertisement revenue has been quite poor. I suspect that people were bypassing the ads and heading straight to the free links in my reviews, essentially leading me to give away too much free traffic.

Scott from Pittsburgh

Where can I purchase well-crafted and laminated credit card-sized versions of your basic strategy tables for blackjack? If you don’t offer them, please consider doing so! Michael Bluejay I'm pleased you asked. You can obtain them through Custom Strategy Cards. These cards contain my blackjack and video poker strategies and are designed to fit nicely in your wallet.

Update as of November 13, 2007: The Custom Strategy Cards website has unfortunately gone under.

Jack from Troy

I noticed your online newspaper column hasn't been updated since June. Are you alright? I hope all is well. I have a basic blackjack strategy card that has been very useful. Do you also have basic strategy cards for electronic poker games? Thank you for your time.

In your last column I'm not certain which internet newspaper column you’re referring to, but I'm doing fine. As a matter of fact, you can find my video poker strategies in an easily portable strategy card at Custom Strategy Cards. While the video poker cards might not be available yet, I know the owner has them, so feel free to ask.

Update: The Custom Strategy Cards business is no longer operational.

Pete from NY

Congratulations on a job well done. I have a question: I noticed in your May 5, 2003 column that you actually perform calculations to determine your blackjack odds. I was rather surprised to learn you aren’t utilizing a computer for simulations. Is that a naive question, suggesting that it would take an eternity for a computer to calculate the outcomes?

Indeed, I calculate the odds for blackjack using a combinatorial framework, examining every potential outcome for player and dealer cards to maximize the expected value at each decision juncture. This process is more complex than simulation but I find it elegantly challenging in recursive programming. Nonetheless, I appreciate that many of my colleagues choose simulation, as modern computers can efficiently run billions of bets, which approaches the optimal strategy results.

John C from Crestwood

I greatly enjoy your site. Earlier today, I was reviewing your experiences with gambling and found that you often end up losing all your deposits, which discouraged me. Then I noticed you were asking for donations, and now I see why!

Since I began gambling online four years ago, I've made about $20,000, with roughly half of that attributed to the Golden Palace. The insights reflected in my reviews are based on my most current experiences, and like many others, I occasionally face losing streaks. However, I've recently won $786 at one establishment and $2,317 at Casino Kingdom. My requests for donations are not to compensate for a gambling addiction but rather to aid in keeping this site available for free to the public. The donations typically come through PayPal, which I often use for purchases on eBay.

anonymous

I tried to locate your casino reviews, but the webpage indicates that they're no longer accessible. I personally appreciate knowing if a casino has policies that could be questionable. What prompted you to remove the reviews?

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Kevin from San Diego, CA

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anonymous

Greetings, Mr. Wizard! I wanted to reach out and express my gratitude for your website, which I've been visiting for nearly a year now. I truly appreciate the effort you put into creating and continually updating it with fresh and valuable content. It's incredible to think of how much time you dedicate to this endeavor.

I have several inquiries to make. First, I'd like to discuss the banners on your site. I'm curious about how we can optimize your earnings through banner clicks. Do you receive compensation based on impressions, unique clicks, or do you have a different payment structure? As of now, I only tend to click on banners that showcase new offerings, but I would be willing to engage with more banners during my visits if it contributes positively to your income.

Additionally, I have some questions regarding your strategy for playing Jacks or Better, as well as the practice mode for the game. I don't mean to come off as dense, but I hope you don't mind my questions. On the Jacks or Better table, where exactly do I find the ranking for a hand that consists of just one high card (A, K, Q, J) without any low cards? My second question is closely related. In the practice game, the optimal move according to the guidelines is to hold the K and Q while discarding the A if the hand has unsuited A, Q, K without any low cards. I would have assumed that keeping the Ace would be the more strategic choice. Can you explain the benefits of discarding the Ace and how one might determine the best play based on this hand and the table?

Thank you, Denis, for your thoughtful comments and your willingness to support the site's financial sustainability. When you first reached out, clicking on my banners was indeed helpful. However, as I update my response for 2013, I now find that new sign-ups are essential for my income. Simply clicking on a banner isn't sufficient unless users register for an account and, ideally, make a deposit.

The reason you see a single line for 'one high card' is that the value of a single jack to an ace approximately equals each other.

Could you please let me know where I might find a printable version of blackjack odds that I can keep in my purse? I'm just starting out and could use some guidance on when to hit or stand.

One suggestion is to right-click on one of my strategy charts, save the file, and then print it. Some casino gift shops offer basic strategy charts that are the size of a business card. However, please be aware that these charts often contain at least one mistake about half the time.

Your website is quite intriguing. Do you earn your income through gambling? Have you ever explored the probabilities involved in trading stock index futures? free craps game I am certainly tempted to delve deeper into futures trading, but my current schedule doesn't allow for it. My income is generated from advertising revenue on this site—please consider clicking on the banners—as well as consulting fees for analyzing new casino games.

Jordan

Fantastic website! Is there a way I could download your pai gow practice software so I don't have to always play online? Thank you in advance.

Results

Can you confirm if the probability numbers for craps, including the odds, are absolutely reliable? Is your work in the gaming industry your full-time job, and how often do you visit Atlantic City? Additionally, how do you simulate billions of hands, spins, and rolls? Is this done through computer software, and if so, which one?

Well, anyone can make an error, but mathematically speaking, craps is relatively straightforward to analyze, and I am very confident in my odds for this game. Yes, gambling, in one form or another, is indeed my full-time self-employed profession. I have visited Atlantic City numerous times over the past few years, but two months ago I relocated to Las Vegas, so I likely won’t be visiting Atlantic City as often now. I tend to prefer a combinatorial analysis approach instead of random simulations whenever possible. Regardless, I utilize my own software, programmed in Visual C++, for the simulations. For generating random numbers, I utilize a...

  1. It's been noted that some poker machines boast payout percentages over 100%. In a prior article, you mentioned that for full pay video poker, the ideal strategy player can expect to hit one royal flush every 40,388 games. Does this imply that a player needs to achieve this number of hands perfectly to realize the advertised payout percentage? I am speaking for the countless video poker enthusiasts who've seen their $20 evaporate in what is labeled a '98%' machine.
  2. No, that isn't the case. Contrary to popular belief, there’s no cycle involved. Each hand is independent of the others. It would take an infinite number of perfect plays to ensure reaching the theoretical 99.54% return.
  3. Here are some statistics for you: Royals represent 1.98% of the return in a 9-6 Jacks or Better setup. Consequently, you can expect the game's return to hover around 97.56% excluding the royals. The standard deviation for a single hand amounts to 4.42, whereas the standard deviation for 40,391 hands—the average number between royal flushes—is 2.20%. Therefore, even after hitting a complete royal cycle, you could still be far from the 99.54% return. There's a 95% probability that you'd find yourself somewhere between 95.24% and 103.85%.

anonymous

  1. The two-player table Regarding pop-up ads, I dislike them as well. However, some form of advertisement is necessary to sustain my work. Consider them to be a small price to pay for the valuable information you're receiving. three to eight Hello! Do you have or recommend any basic strategy cards for blackjack? Previously, I bought some from Winning Publishing NV. Your site is excellent.
  2. Your timing with this inquiry is perfect! Marsha Ness, who runs Custom Strategy Charts, is now ready to offer laminated blackjack and Spanish 21 strategy cards. The strategies are sourced directly from me, with a wide variety tailored to different rules. Currently, electronic payment options are not available, so you'll need to send a check via mail.
  3. Update: Since the time this question was published, the Custom Strategy Cards service has unfortunately gone offline. May 1999 I thought you had banned the Golden Palace Casino, yet I just received an email from you promoting them. What’s the explanation for that? 2005 season , which was an abject failure.

You're not the only one who has raised concerns. My advertising partner believed my issues with them were a thing of the past and accepted their advertisement. I wasn't pleased about this, and I apologize for the oversight. I hope this won’t be repeated.

Mark from Pahokee

No, I have pondered it, but I'm concerned that if I ordered a large supply, I would be stuck with most of them.

I recently stumbled upon your site and it's really impressive! I noticed that online casino reviews have been taken down—will they be reinstated?

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MustangSally

I’m uncertain about that. The site has been underwhelming in terms of advertising revenue. I suspect this is partly because users were ignoring the ads and heading directly to the free links in the reviews, effectively giving away too much traffic for free.

Popeye crop

Where can I purchase quality printed and laminated credit card-sized versions of your basic strategy charts for 21? If you don't offer them, I would love for you to start! Wizard of Vegas .