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Ask The Wizard #27
I must express my disagreement with your earlier remark concerning how random number generation works on computers. It's a fact that sequences may eventually repeat, yet this outcome can be influenced. The key is to initialize the seed correctly. For instance, if you’re working on a UNIX system, you might set the seed based on the number of seconds that have elapsed since January 1, 1970, which is a variable that keeps updating. While Visual C++ and J++ usually reset to a new random seed every time they are executed, I recommend manually setting the seed in your program. For example, you could update the random seed each time a new deck is 'dealt' by using the current machine time or a similar approach. This way, even if the number sequence loops, you’ll be selecting somewhat 'random' values along the way, avoiding a complete cycle.
When utilizing Visual C++, it's evident that the seed remains constant. If the program receives the same input, the output will consistently match across random simulations. From what I gather, this was Microsoft's intention to allow for precise replication of experiments. My experience with Visual J++ suggests a different approach, as I’ve noticed varied outcomes in my games; otherwise, you’d witness the same sequences of hands repeatedly.
Postscript: Since I wrote this, I've discovered a slower yet much more effective method for generating random numbers. Click here for more information.
I've heard of a casino located in the Seattle area that features six-deck payout odds when placing a match bet against the dealer in Spanish 21 using an eight-deck shoe. I'm interested in knowing how this impacts the house edge.
This lowers the house edge from 3.06% to 1.42%.
If I recall correctly, I read something about the probability of two people in a group of twenty sharing the same birthday being less than 50%. Is that accurate?
Calculating the chances of 20 individuals each having distinct birthdays (not taking leap year into account) gives us approximately (364/365)*(363/365)*(362/365)*...*(346/365) = 58.8562%. Thus, the likelihood of at least one shared birthday among them is about 41.1438%. It's worth noting that you only need 23 individuals for the odds of a shared birthday to exceed 50%.
I often play pai gow poker in Atlantic City, and I frequently witness players managing two hands at once. My question is whether being able to see 14 cards out of a total of 53 provides the player with any competitive advantage. If so, how significant is this advantage, and what adjustments in strategy might it necessitate? Any guidance would be appreciated.
In pai gow poker, the dealer sometimes sets aside a dragon hand, offering it to each player individually. This scenario mimics playing two hands and is likely what you've observed. However, the rules for playing the dragon hand typically dictate that it must be arranged according to the house’s prescribed method.
Even if a player was able to leverage the information from those 14 cards when arranging their hand, I doubt it would provide a considerable edge, and making the most out of that information could be quite complex.
In Spanish 21, you mention that using your basic strategy results in a house edge of 0.34% when the dealer stands on soft 17. How is this percentage affected by the super bonus? Specifically, what would the house edge look like without including the super bonus, and how likely is it to trigger the super bonus on a given hand?
For a game with six decks, the chances of hitting a super bonus are estimated at 1 in 668,382, whereas an eight-deck game has odds of 1 in 549,188. The house edge without the super bonus would increase by 0.03% in either case.
Fantastic website, Wizard! I like to think of myself as a bit of a wizard too. Quick question—I enjoy playing blackjack at casinos, mainly in Las Vegas, and I've been employing the Hi-Opt 1 counting method without much success. According to Casino Player Magazine, August 2000, page 50, a comparison table suggests that Uston APC, Halves Count, Revere APC, Advanced Omega 11, and Hi-Opt II are some of the most profitable systems. Could you share your thoughts on these and the point values associated with each?
This question could fill an entire book. I apologize for only being able to scratch the surface here. In Uston's 'Million Dollar Blackjack', page 107, he details the following card values for the Uston Advanced Point Count:
Uston Advanced Point Count
| Card | Value |
|---|---|
| 2 | +1 |
| 3 | +2 |
| 4 | +2 |
| 5 | +3 |
| 6 | +2 |
| 7 | +2 |
| 8 | +1 |
| 9 | -1 |
| 10 | -3 |
| ace | counted separately |
It's evident that this is a more robust system compared to {-1,0,+1} systems like Hi-Opt I. There are numerous methods to assess the strength of any system. In my view, serious players should adopt the most powerful system they are comfortable with. It's better to master a level 1 system (like Hi-Opt I) than to poorly execute a level 2 system (such as Hi-Opt II).
I have a suggestion, dear Wizard—when you next publish your book, could it be made smaller? Perhaps a pocket-sized edition suitable for carrying in a purse?
My current publication measures 5.5\" x 8.5\". I regret to inform you that I don't plan to release another anytime soon.
Are Indian casinos held to the same operational standards as their non-Indian counterparts? Is the payout regulated on a monthly basis as a whole or on a per-machine basis? If it is overall, couldn't a casino adjust the payouts on individual machines at any hour of the day or week?
When I step into one of these 'Indian' casinos, I can often stand for five minutes, absorbing the sounds of the bells and tunes, and predict the likelihood of having a successful day. With 300 slot machines all programmed with fixed payouts, you'd expect a consistent frequency of sounds with the same number of players, but that’s not the case. I suspect all the newer machines are connected and adjusted according to psychological factors affecting players.
Generally, Indian casinos maintain a self-regulated system. There is usually a tribal commission that hears disputes, but ultimately, the commission members have their interests to consider.
Don’t presume that there’s any guaranteed minimum payout on the slot machines. However, economic principles would suggest that a return that is too low would become apparent to players, who would likely not return if they frequently lost money too quickly. Additionally, it wouldn’t be good business practice to constantly alter the slots' payout levels drastically.
Your hypothesis about sound levels is quite intriguing; I had never approached it from that angle before.
How can casinos program their slot machines to ensure a specific payout percentage when the machines operate from a random number generator? It seems like there would be no way to anticipate which number or combination (winning or losing) will come next.
Casinos don't actually program their machines to deliver a set payout percentage; instead, they adjust the weighting of the reels to achieve a desired theoretical return. While the actual return can vary significantly in the short term, mathematics dictates that over numerous spins, the actual return will converge to the theoretical expectation.
The casino in Biloxi, Mississippi, features single-deck blackjack dealt from the bottom of the deck. What is the house edge for this variation? Additionally, does the basic strategy for blackjack still apply in this scenario? By the way, in this version, blackjack pays even money.
Dealing from the bottom of the deck doesn't assist the basic strategy player but can give a substantial advantage to card counters. The basic strategy remains unchanged. However, this game might catch the interest of counters. Vegas World (now known as the Stratosphere) in Las Vegas had a similar setup, but I don’t believe counterplayers ever took it seriously due to adverse house rules, like paying even money for a blackjack.