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Ask The Wizard #344
Let 0 < a < b. Which is more a^b or b^a?
The specific outcome is contingent upon the values of a and b, yet two general principles will suffice for most scenarios.
If a > e, then a^b > b^a
If b < e, then a^b < b^a
When a is less than e and b is greater than e, there isn't sufficient data to make a judgment.
Here is the solution (PDF).
A grenade is hurled into an infinite abyss, and on average, it detonates after six seconds. The duration before detonation possesses a memoryless characteristic, meaning that the likelihood of an explosion occurring at any specific instant remains constant regardless of how long it has been since the safety pin was removed. In simpler terms, its lifespan adheres to an exponential distribution. Assume This query has sparked discussion in my forum at Earlier today, I spent approximately six hours playing craps and observed the dice stacking on top of one another on two occasions. What are the chances of that happening? acceleration of 32 feet per second.
Here is my full solution (PDF).
I consulted three different sources, two of whom boast a cumulative experience of 35 years in dealing craps. Together, they have witnessed around 1 to 1.1 million dice rolls and have observed stacked dice approximately ten times. This assumes a playing frequency of Wizard of Vegas .
. With that in mind, I estimate that the likelihood of a single roll resulting in stacked dice is roughly one in a million.
Considering the casino and the time of day during your gameplay, I can infer that the number of players was likely low. I estimate around 215 rolls per hour during your session. Using that, coupled with the probability for any given throw, I approximate the odds of witnessing stacked dice twice in 1,290 rolls to be 1 in 1.2 million. 140 rolls per hour , you clarify that even though there are 2,598,960 possible combinations for starting hands in video poker with a standard 52-card deck, only 134,459 distinct hand categories need to be examined.
I'm curious about the number of categories in joker poker.
I consulted three different sources, two of whom boast a cumulative experience of 35 years in dealing craps. Together, they have witnessed around 1 to 1.1 million dice rolls and have observed stacked dice approximately ten times. This assumes a playing frequency of Wizard of Vegas .
In your video poker programming tips For this inquiry, I consulted my respected colleague, Gary Koehler, who specializes in the mathematics of video poker. Below are his insights, based on the number of jokers involved:
Strategies and insights rooted in mathematical principles for various casino games, including blackjack, craps, roulette, and many more available for play.
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- 1 Joker: 150,891
- 2 Jokers: 169,078
- 3 Jokers: 189,189
- 4 Jokers: 211,406
- 5 Jokers: 235,925