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You can move this to general science or somewhere. I just posted it here because physicists are good at math.Anyway, I've been reading two books at the same time that have nothing to do with each other, totally different topics. But curiously, both authors used the same mathematical example to illustrate a point, but with different solutions. The situation is this: You are playing a guessing game, where you have to guess which light will flash next, green or red, and it's random, but set up so that it flashes red 80% of the time and green 20% of the time, and you are aware of this. A) Should you always guess red? Or B) should you answer red 80% of the time and green 20% ? One author said A will give you more correct answers, and another said B will.

My initial response to this is as red flashes 80% of the time by guessing red every time is going to mean you will be correct 80% of the time.

If the lottery is truly random, then it shouldn't make any difference if you choose the same number or not.

Here's a way to see this experimentally. Take a coin and flip it 100 times and record the value of each flip on a piece of paper. Each time you flip the coin, call either heads or tails each time. Right that down too and then record if you won or loss each time.At the end of the 100 flips determine how many times you called it correctly. Now determine how many heads came up. Which number is greater?

If you're correct, try the opposite for the next flip. (turns out to give the exact opposite results as the previous trial)

Quote from: Pmb link=topic=49168.msg420482#msg420482Here's a way to see this experimentally. Take a coin and flip it 100 times and record the value of each flip on a piece of paper. Each time you flip the coin, call either heads or tails each time. Right that down too and then record if you won or loss each time.At the end of the 100 flips determine how many times you called it correctly. Now determine how many heads came up. Which number is greater?Oh, Evan beat me by a couple of minutes []Sorry, I'd rather do this electronically, than with a coin.So, I whipped out a quick program using the random number generator.1,000,000,000 "flips".4 paradigms.Count Heads / Tails (same as if had guessed heads or tails).Every flip, make a new random guess.Start with heads. If it is "right", then guess the same the next time. If it is "wrong", then make the opposite guess the next time. (This is the same as guessing the next flip will be the same as the last flip)If you're correct, try the opposite for the next flip. (turns out to give the exact opposite results as the previous trial)All results came between 49.998% & 50.002% Of course there were some minor differences between different methods which I'm attributing to flaws in the pseudo-random number generator being used by the system.That is a point for lotteries though. You may be able to "beat the odds" if it has a computer generated random number generator, but assuming the spinning balls that are frequently used by lotteries actually give true random numbers, then it isn't so easy to beat the odds.Note, by flipping a real coin, it is also possible that one doesn't get it completely randomized between flips, so the probability of the next flip may be dependent on the last state.

If I'm doing my calculations right, the results of 1,000,000 flips should have a standard deviation of 500 heads off from the mean value of 500,000 heads. This would put it at 49.95% heads and 50.05% heads within 1 standard deviation. In other words, it's likely that 49.998% to 50.002% guessed correctly is just statistical fluctuation, not an issue with the RNG used.