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Truly Random Numbers
I've been working to create an Excel Spreadsheet to create lottery numbers drawn in picture form. Basically a grid. I'd speculate that if lottery numbers are random then in a perfect situation would be a number after being drawn would not be drawn again until all other numbers have been drawn. We know this not to be true. What in theory makes the lottery numbers drawn is that we can't consistently predict what the next drawn numbers would be. So far I'm using the Spreadsheet for Michigan's Lotto
Dec 16, 2023, 12:27 pm - SwingTrader1941 - Mathematics Forum

Box odds questionReply
it seems to me that you understand how to figure the odds, and the underlying question is how close will the actual drawing match the mathematical odds. my answer is fairly close over time, but about useless for what will happen in the next drawing. when you see under or over performing groups it may be your definition of the groups or it may be just random being a bit random. think of this as a very rough pointer at best. you say these numbers are based on 17000 drawings. if you only use 1000 d
Aug 11, 2023, 4:11 am - phileight - Mathematics Forum

"Post-Game Review" - $1.58B MM Jackpot This WeekReply
At least. You can fairly easily calculate conditional probabilities and EVs given the assumption that the player never hits 5 main balls (with or without Megaball) over a lifetime. Just keep the same numerators and subtract off 25 from the denominator from my posted table to get the (new) conditional probabilities for the lower tier prizes. How likely is that 5 + 0 or 5 + 1 is never hit? Let's say a player buys 6 Quickpick tickets per week (3/drawing). The player does that for 40 years. That
Aug 13, 2023, 1:09 pm - Orange71 - Mathematics Forum

Mega Millions Just The JackpotReply
Ponder that the winning numbers for PB and MM are selected by mechanical lotto machines, not PRNGs. The PRNG algorithms only select Quick Picks. Any slight bias in the algorithm is going to have such a very minor effect on the Binomial assumption it won't practically matter. The players with unique combinations selected on play slips will have a more significant effect on deviation from the Binomial Distribution. There was one Jackpot winner in last night's $1 Billion Power Ball drawing. Per
Jul 20, 2023, 8:18 pm - Orange71 - Mathematics Forum

Monty Hall Problem and Implications Explained
The Monty Hall problem is a famous case study in the application of Probability, specifically the concept of Conditional Probability. In simple terms Conditional Probability is the probability that something will occur given the additional information that something else has occurred. If something else is known to have occurred, it may or may not affect the probability of something . Examples of the probability of something not being affected by something else are (a) the outcome of the n-t
Mar 28, 2024, 9:56 pm - Orange71 - Mathematics Forum

"Post-Game Review" - $1.58B MM Jackpot This Week
A single winner in Florida hit the $1.58B Mega Millions this week. The cash value (I saw on TV anyway) was about $783M. This begs the question: playing a regular $2 ticket, did a player have a positive return expectation (expected value of return $2 bet)? Answers: 1. Before income tax - yes, roughly $0.11 gain per $ bet (about +11% return) 2. After income tax - no, roughly $0.28 loss per $ bet if you assume a 35% tax rate on winnings. (about -28% return) First, I looked up the nu
Aug 12, 2023, 12:53 pm - Orange71 - Mathematics Forum