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Showing posts from March, 2021

Expected Winnings When Playing Keno

 Overview It's common knowledge that the entity that runs a gambling game has set it up so they don't lose in the long term. Not all states' Keno games are created equal, though. Below is a detail of long-term expected winnings (technically, all are losses) when playing Keno in different states along with the calculation methodology. Summary Table 1. Expected long-term earnings per draw in various states. The game highlighted green is the best choice (least loss). The 1-Spot game is typically the worst, so the spot highlighted red is the 2nd-worst. State 10-Spot 9-Spot 8-Spot 7-Spot 6-Spot 5-Spot 4-Spot 3-Spot 2-Spot 1-Spot Winnings Page Kentucky -$0.36 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.34 -$0.50 Link Maryland -$0.43 -$0.44 -$0.41 -$0.40 -$0.44 -$0.46 -$0.42 -$0.38 -$0.40 -$0.50 Link Michigan -$0.36 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.35 -$0.34 -$0.50 Link Ohio -$0.36 -$0.35 -$0.35 -$0.35 -$0

The Electrostatic Charge Is a Phenomenon Similar to Gravity

In  Einstein's elevator thought experiment , he imagined a person in a free-falling elevator. If they weren't able to see the Earth approaching ever closer, they would think they were in deep space and not accelerating. Similarly, if the elevator were to accelerate in deep space at 1 g, they may think the elevator is stationary at Earth's surface. This PBS Spacetime episode  and  this Science Asylum episode  explain the phenomenon of space-time warping due to mass and its effect on nearby objects. I posit that we can broaden both the thought experiment and explanations of the videos to incorporate the electrostatic force. In deep space, a negative charge will accelerate toward a positive charge in a "free fall", i.e. neither will feel a force while accelerating toward each other. If you put an electrically neutral and permeable membrane in front of the negative charge to hold it back, it would feel the force of the membrane pushing back on it, like a pseudo-gravit

A Grandpa and a Dog

Background My friend sent me this TikTok  in which the OP calculated the probability that his grandpa, 84, and his dog, 15, died within two days of each other. OP's Analysis Grandpa was alive for D = 84 years = 30,660 days. Dog, d = 15 years = 5,475 days. The probability that Grandpa died within any 2-day period, P = 2 / D. Probability for Dog, p = 2 / d. The probability that Grandpa and Dog died within the same 2-day period = P ⋅ p = 1 in ~42 million. Issues with OP's Analysis "Within 2 days of each other" is a 4-day period, not 2 days. The probability of either dying on a given day is not evenly distributed throughout their lives. Dog was born when Grandpa was age 69, so the probability of both dying days apart is 0% up until Grandpa turns 69. Vastly More Accurate Calculation Answer The probability P that Grandpa and Dog died within 2 days of each other is 0.0453% or 1 in about 2,200. This is a factor of 19,000 more likely than OP suggests. If there are 1,530 simil