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Ask The Wizard #141
It's interesting to ponder why individuals hold fast to their faith in gambling strategies, believing they can outsmart the house despite knowing the odds. While many players may not understand the underlying rules or probabilities, there are those of us who are well-informed yet still cling to the idea that certain systems, timing, or other flawed reasoning can tilt the odds in our favor. Despite your background in mathematics, your experiences must provide you with some understanding of what drives such beliefs in the gambling community, wouldn't you agree?
That's an insightful inquiry. I've encountered a number of individuals who strongly advocate for various systems, and they all share a noticeable degree of arrogance. Even though they may have only scraped the surface of mathematical understanding, they often presume to possess knowledge that surpasses that of distinguished mathematicians. This stubbornness to disregard contradicting evidence isn't unique to those chasing betting systems; the more ludicrous a belief becomes, the more fervently it is held, and there are plenty of absurdities for those lacking critical thinking skills to latch onto.
I've been playing online poker for quite some time and I've observed a frequent occurrence of strong hands, particularly high pocket pairs (like Aces, Kings, Queens, and Jacks). Statistically, one should expect to receive pocket Aces approximately once every 220 hands; however, I feel that I'm experiencing them much more frequently. Some of my friends have (reportedly) kept track of their pocket Aces and found an average of about once every 125-150 hands over a span of 10,000 hands. This seems to fall well outside the standard deviation, which raises my suspicions about the integrity of the game. Have you conducted any studies on this matter? Also, what would be the probability of achieving an average of pocket Aces every 150 hands out of 10,000 (meaning 67 occurrences of pocket Aces)?
The likelihood of drawing pocket Aces is calculated as combin(4,2)/(52,2) = 6/1326 = 1 in 221. Thus, over the course of 10,000 hands, it's expected to get pocket Aces approximately 10,000/221 = 45.25 times. The standard deviation for 10,000 hands would be calculated as (10,000 * (1/221) * (1 - (1/221))) = 6.71149. Having 67 pocket Aces would fall (67 - 45.25)/6.71149 = 3.24 standard deviations above what is predicted. The likelihood of encountering results this extreme or more is 0.06%, or roughly 1 in 1673. combin Are you a true Packers supporter? I can relate; it seems like your loyalty is affecting your betting decisions, especially since the Packers aren't consistently performing well for you. It might be worth considering this perspective.1/2However, my reasoning isn't based on team loyalty. After evaluating performances, my program ranked them as the fifth best team following the end of the 2004 season, and I continued to use that rating as I moved into the 2005 season. It's possible that my system is slow to adapt to recent performance trends, which is something to reflect on.
Greetings, admirable Wizard! I truly appreciate your website and the insightful knowledge it has provided me. Today, I seek clarity on the mathematics behind the odds of specific combinations of wagers. For example, betting groups of two on both the 6 and 8 in craps, or a set of four bets considered as an 'inside' bet in craps. We calculate the odds for betting on either the 6 or the 8 as ((5/11)*7 + (6/11)*(-6))/6 = 1.515%. But what happens if we place bets on both the 6 and the 8 simultaneously? Using a similar formula: (((10/36)/(10/36+6/36))*7+(((6/36)/(6/36+10/36))*-12))/12 = -1.04167%. There are 10 chances to win 7 and 6 chances to lose 12, correct? Am I mistaken? I appreciate you taking the time to consider my question. NFL picks I receive numerous inquiries about combinations of bets in craps. Normally, I don’t engage with these questions, but your respectful address as 'the great and powerful Wizard' certainly enhances your chances of receiving a response. The flaw in your calculations lies in the fact that not every bet resolves simultaneously. When you win on either the 6 or the 8, you take the other bet down, thereby lowering your expected loss due to betting less. Thus, while your calculations are accurate, you're comparing two concepts that aren't directly aligned.
Would you be open to conducting a thorough examination of Texas Hold’em Bonus? It seems to be gaining popularity across various casinos in Atlantic City and is also present in the Flamingo Las Vegas. Thank you for your consideration!
Coincidentally, I currently have four computers processing extensive data on that game. The sheer number of possible combinations is immense, requiring approximately 56 days of computational time to analyze thoroughly. I anticipate having the analysis ready around October 20.
What is the probability of a dealer landing on 5 instances of the same number within 10 rotations of the roulette wheel?
The chances of any given number appearing exactly 5 times in 10 spins, in a double-zero roulette scenario, can be estimated using 38 times the probability formula.
I'm thinking about the situation of a person who approaches an active craps table wishing to join in. While I understand that the history of the table holds no real weight, I wonder why you wouldn't advocate for placing a come bet right from the start? My comprehension suggests it would yield the same expected result as waiting for a new come-out roll, yet the eager bettor wouldn't have to bide their time.
You're absolutely correct. A come bet would indeed offer the same potential without requiring any waiting, and I should have pointed that out.
I doubt that. I have set the odds at yes +240, no -300. combin (10,5)*(1/38)5*(37/38)5= 1 in 359275.
A follow-up to the recent question I have a straightforward inquiry related to the online gaming realm. A casino claims that their RNG provides a return of, for example, 96.7%. We also know that payment processors typically charge these establishments, say around a 3.5% transaction fee on drop amounts (not on the take). So, how do these operators actually generate profit, or are the RNGs misleading us?
The 96.7% return pertains to the cumulative total of all bets placed, while transaction fees typically apply solely to deposits and withdrawals. Players tend to recycle the same funds, thus betting far more than they initially deposit. As I detailed in my column on September 18, 2005, a player with a bankroll of $10,000 betting $5 at a time could cycle through roughly 1.5 million dollars. In this scenario, the casino's profits are calculated based on 1.5 million in total bets, while their expenses are merely based on the $10,000 received.
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