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Ask The Wizard #79
Could you explain the expected return on Blackjack if a player bets all their money on a single hand without funds to split or double down? Thank you.
Not being able to double or split your bets adds an additional 1.9% to the house edge. This highlights the importance of always having enough money for splitting or doubling when playing.
Hello Sir, we are dedicated Keno enthusiasts. We strongly believe that if we play multiple Keno machines with the same numbers, our chances of winning are significantly enhanced. Could you provide us with some statistics to validate our belief? Thank you.
Your expected return remains constant, no matter how many games you engage in. While playing more machines does increase your chances of hitting a number, if all of them fail, your losses multiply.
I've been enjoying Blackjack for some time, generally sticking to a basic strategy and betting a flat amount each hand. Occasionally, I might increase my wager because I get a feeling that my next hand will be a winning one. I believe many casual players do the same from time to time. I came across one of your previous articles where you discussed the odds of experiencing consecutive losses in your August 4, 2002 column. You know how those emotional thoughts arise while gambling (maybe they don’t for you), thinking to yourself, 'I’m overdue for a win!'
That article seemed to break down the mathematics behind that sense players often feel. In your example of a player who lost 8 hands in a row, the odds were approximately (.5251^8, or about 1 in 173). My query is, what does this imply? Does it mean that during a gaming session, I could expect one out of every 173 to result in an 8-hand losing streak? Or does it indicate that any given loss has a 1 in 173 chance of being the first in a series of 8?
I understand that my inquiry may sound like I'm looking for a mystical betting system, and I know that no betting structure can change the house edge. Still, I'm genuinely intrigued. After all, occasionally increasing my bet does heighten the thrill, and it seems somewhat logical to think that after a sequence of losses, one is 'due' for a victory.
I see no issue with raising your bet when you feel lucky. What's crucial is that you play your cards wisely. Unless you’re counting cards, you're free to set your bets as high as you wish. As I've often said, all betting systems ultimately have the same worthlessness, meaning that playing by gut feelings is just as effective as consistent flat betting in the long term. When I mentioned the likelihood of losing 8 consecutive hands is 1 in 173, I meant that for the next hand, the chance of facing 8 consecutive losses remains 1 in 173. The risk of consecutive losses increases with longer play sessions. I hope this clarifies your concern.
Are there any methods for cheating at slot machines?
Absolutely, there are numerous ways to cheat. For instance, inserting counterfeit coins is a simple tactic. However, be aware that in Nevada, cheating in a casino is punishable similarly to bank robbery, or so I’ve heard. To be clear, I strongly disapprove of cheating in any form.
Mabuhay!! What an incredible website!!! I've gained so much knowledge from you! If I hadn’t learned the mathematics behind casino games, there’s a good chance I would have developed a gambling addiction by now. I used to play to win, but after discovering the house always has the edge, I learned to enjoy the experience instead. I am curious if you are acquainted with Super 6; it’s a no-commission version of baccarat that offers a payout of 1:2 on a winning 6. What is the house edge for both banker and player in this game? Additionally, there is a side bet that pays 12-1 on a winning 6; does that qualify as a bad bet? Thanks.
Thank you for your kind words. I have addressed the concept of commission-free baccarat in my baccarat section. Indeed, the winning 6 is considered a poor bet. The probability of a banker achieving a winning 6 is 5.39%, while for the player, it's 6.26%. The house edge for the banker stands at 30.00%, and for the player, it is 18.68%.
Greetings. I've been an enthusiastic roulette player for several years, and for the first time ever, I’m contemplating trying a roulette betting system. I understand how you feel about these so-called 'systems' and the scammers promoting them, and I share those sentiments, but I have encountered two systems that seem worth considering.
The first is the 3q/A-strategy detailed in R.D. Ellison’s book, \"Gamble to Win: Roulette,\" which boasts a verified win rate of 7.94% based on 7500 spins. This system was developed alongside \"Spin Roulette Gold\" by Frank Scoblete and \"Roulette System Tester\" by Eric St. Germain.
The second system is Don Young’s roulette strategy, which has been validated to outperform the Roulette System Tester from Zumma Publishing, based on 15000 spins.
I have to admit that I’m still a bit wary about investing in these systems, but since they have shown consistent results over time, I see no obvious reason why I shouldn’t give them a shot. I mean, surpassing these benchmarks has to have some significance.
What are your thoughts on these systems? Do you think I should give them a try?
Thank you so much! Have a wonderful day. Best regards.
7500 spins? Is that really the number? Anyone can demonstrate a 7.94% profit from the total amount bet over 7500 spins with an aggressive betting strategy. The same goes for 15000 spins. Most betting systems are structured to produce a lot of small winnings while experiencing a few significant losses. A system requiring a substantial bankroll can easily navigate 15000 spins and still show a profit temporarily. Eventually, the significant losses will occur, and the system won’t sustain its success. In fact, those substantial losses could happen right at the start. The only way to thoroughly test a system is through billions of trials. My stance on these systems is consistent: they hold no true value. I don’t mind you trying them, but I strongly oppose anyone investing even a cent into the pockets of those who sell them.
Note: Please refer to the follow-up pertaining to this inquiry in the next column .
Dear Sir, I've gone through your FAQs with great interest. I have a query of my own. In baccarat, how frequently can one expect to witness a Banker/Player winning streak of nine consecutive wins? Could you break down the mathematics for me? Thank you.
The probability of a single Banker win is approximately 0.50682483, whereas the single Player win is around 0.49317517, disregarding ties. Hence, the chance that the next 8 hands will yield a Banker win, while skipping ties, is 0.50682483, which calculates to approximately 0.004353746. The chance for the Player is calculated at 0.49317517.8I have an interesting calculation to discuss. While playing Deuces Wild Video Poker, I got dealt an awful hand. Upon discarding all five cards, I was fortunate enough to draw four deuces, earning 1,000 coins! What is the probability of drawing 4 Deuces after discarding all five cards? Thank you for your time, and keep up the fantastic work on your website! P.S. On that same machine, I switched to Deuces Wild Bonus Poker and was dealt 3 wild cards along with the 4 and 5 of diamonds (straight flush). After discarding the 4 and 5, I managed to draw 4 deuces with an Ace for another 2,000! What a lucky occurrence! This happened at Soboba Casino in Southern California.8= 0.003499529.
No worries! There are combin(47,5)=1533939 ways to choose 5 cards from the remaining 47 in the deck. Out of these, 43 combinations will yield four deuces (the 5th card has 43 different possibilities). Therefore, the likelihood of drawing four deuces on the next hand is 43/1533939 = 1/35673 = 0.000028032. The odds of drawing a fourth deuce after keeping three is (47-1)/combin(47,2) = 46/1081 = 0.0426. In my
you can observe the probability distribution in Deuces Wild regarding the number of cards drawn for a particular hand. For instance, 2.62% of all four deuces will occur when all four are drawn at once. The probability of this outcome on any given hand stands at 0.000005. For additional information on the combin function, please consult my section on video poker appendix 5 Mathematically accurate strategies and data related to casino games such as blackjack, craps, roulette, and countless others. probabilities in poker .