Teaching an intelligent guy about a basic statistics concept

[Chino Brown]

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Usually, the explanation of "each individual coin flip is even money" for either heads or tails assuming an unbiased/fair coin...and that T-T-T-T-T-T-T-T-T-T is as likely for a "random walk" as, say, H-T-T-H-T-T-H-T-H-H. All tails just looks funny; we are pattern recognizing machines after all, oftentimes regardless of any value in meaning.

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This is a good point. I had a very good friend who was well trained in math and statistics (he became a chartered accountant in the end). We were talking about lotteries (powerball, 6/49 type). I mentioned that one could just pick numbers 1, 2, 3, 4, 5, 6. His initial reaction was, "that's stupid, what are the chances of that happening?". To which I answered, "just as likely as any other numbers". He had to think about it for a while before he convinced himself that I was right.

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As it turns out, though, picking 1-2-3-4-5-6 is stupid, since you are punished for picking the same numbers as others.

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Umm, wouldn't it be less likely for someone else to pick the #'s 1-6?? Most people use the line of logic that above posters friend uses, and assume that something as simple as that number pattern would be less likely to occur.

[soon2bepro]

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Please. Your friend is wrong. If you flip a coin, get heads and flip it again, everybody knows you're more likely to get heads.


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I meant a fair coin.

[soon2bepro]

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To quote John McClane

"[censored] Calfornia"

Also, on the Martingale crap. Isn't it profitable- given no betting limit and an unlimited bankroll?

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This wasn't the topic, but just to clarify, martingale is only profitable if you have an infinite bankroll and an unlimited bet limit, but infinite is only a concept. however, no matter how large the number, if you have a limited bankroll or bet limit, it's not profitable. You can have a Googolplex dollars or betting limit, and still it won't be profitable. You need a truly infinite bankroll and no betting limit at all for it to be profitable. And as we know, infinite doesn't really exist.

[threeonefour]

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To quote John McClane

"[censored] Calfornia"

Also, on the Martingale crap. Isn't it profitable- given no betting limit and an unlimited bankroll?

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This wasn't the topic, but just to clarify, martingale is only profitable if you have an infinite bankroll and an unlimited bet limit, but infinite is only a concept. however, no matter how large the number, if you have a limited bankroll or bet limit, it's not profitable. You can have a Googolplex dollars or betting limit, and still it won't be profitable. You need a truly infinite bankroll and no betting limit at all for it to be profitable. And as we know, infinite doesn't really exist.

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to be more accurate, its not profitable with an infinite bankroll because profiting implies having an increase. if you have an infinite bankroll then win 100million more dollars, you still just have an infinite bankroll. if you have an infinite bankroll is doesn't matter what strategy you take, as long as you bet finite amounts, you will always have an infinite bankroll.

so saying it works if you have an infinite bankroll is silly on multiple levels.

[Benholio]

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Usually, the explanation of "each individual coin flip is even money" for either heads or tails assuming an unbiased/fair coin...and that T-T-T-T-T-T-T-T-T-T is as likely for a "random walk" as, say, H-T-T-H-T-T-H-T-H-H. All tails just looks funny; we are pattern recognizing machines after all, oftentimes regardless of any value in meaning.

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This is a good point. I had a very good friend who was well trained in math and statistics (he became a chartered accountant in the end). We were talking about lotteries (powerball, 6/49 type). I mentioned that one could just pick numbers 1, 2, 3, 4, 5, 6. His initial reaction was, "that's stupid, what are the chances of that happening?". To which I answered, "just as likely as any other numbers". He had to think about it for a while before he convinced himself that I was right.

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As it turns out, though, picking 1-2-3-4-5-6 is stupid, since you are punished for picking the same numbers as others.

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Umm, wouldn't it be less likely for someone else to pick the #'s 1-6?? Most people use the line of logic that above posters friend uses, and assume that something as simple as that number pattern would be less likely to occur.

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I'd be willing to make a large wager that the numbers 1-2-3-4-5-6 are picked more than the vast majority of arbitrary numbers.

Think of it this way, if there are say around 14 million combinations, you only need more than 1 in 14 million ticket buyers to think its funny/cool/smart to play 1-2-3-4-5-6 for it to become more frequently picked than an arbitrary number. (Wanna play the numbers from Lost? You are playing for a fraction of the jackpot now...)

For this reason, any number that you can come to by some simple mathematical system or pop-culture refernce, etc, is automatically worth less than a 'random' or seemingly arbitrary number with no special meaning.

Heck, if you really wanted to get the most +EV lottery numbers, you would probably write your own random number generator, and throw out any results that have the number 3, 7, 13.. and throw out any recognizable sequences (2-4-6-8-10-12) etc. But this is going way beyond the topic.

[soon2bepro]

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To quote John McClane

"[censored] Calfornia"

Also, on the Martingale crap. Isn't it profitable- given no betting limit and an unlimited bankroll?

[/ QUOTE ]

This wasn't the topic, but just to clarify, martingale is only profitable if you have an infinite bankroll and an unlimited bet limit, but infinite is only a concept. however, no matter how large the number, if you have a limited bankroll or bet limit, it's not profitable. You can have a Googolplex dollars or betting limit, and still it won't be profitable. You need a truly infinite bankroll and no betting limit at all for it to be profitable. And as we know, infinite doesn't really exist.

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to be more accurate, its not profitable with an infinite bankroll because profiting implies having an increase. if you have an infinite bankroll then win 100million more dollars, you still just have an infinite bankroll. if you have an infinite bankroll is doesn't matter what strategy you take, as long as you bet finite amounts, you will always have an infinite bankroll.

so saying it works if you have an infinite bankroll is silly on multiple levels.

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I guess you're right, but I meant that you win more money than you lose, not that you increase your bankroll.

[southerndog]

1.)What u need to stress to your friend is that the AVERAGE OBSERVED should head towards the TRUE AVERAGE. Not so much the TOTAL. As others have pointed out, if you flip ten heads in a row... your average is 100% ..Now imagine the next two flips.. on average, one heads, one tails, so now your average is 1/12, closer to 50% then 100%.. You still have 5 flips more than you would expect.

2.) Tell your friend to think of it like a coffee club. You pay $5 to get your first cup with a mug that you keep. Every cup there after costs you $0.25. So, after your first cup, your total and average is $5. Your second cup is .25, so your total is $5.25, but your average has dropped to $2.62. On your third cup your Total is $5.50, and your average is $1.83... So over time, that $5 investment that you made never goes away, but the average you spend on each cup keeps going down.

[tarheeljks]

it seems like an explanation of conditional probability would end the discussion.

[yukoncpa]

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I'd be willing to make a large wager that the numbers 1-2-3-4-5-6 are picked more than the vast majority of arbitrary numbers.

Think of it this way, if there are say around 14 million combinations, you only need more than 1 in 14 million ticket buyers to think its funny/cool/smart to play 1-2-3-4-5-6 for it to become more frequently picked than an arbitrary number. (Wanna play the numbers from Lost? You are playing for a fraction of the jackpot now...)

For this reason, any number that you can come to by some simple mathematical system or pop-culture refernce, etc, is automatically worth less than a 'random' or seemingly arbitrary number with no special meaning.

Heck, if you really wanted to get the most +EV lottery numbers, you would probably write your own random number generator, and throw out any results that have the number 3, 7, 13.. and throw out any recognizable sequences (2-4-6-8-10-12) etc. But this is going way beyond the topic.


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According to the lottery commission, the first 6 or seven numbers and the last 6 or 7 numbers are picked thousands of times per week. You want to avoid the numbers 1 through 12 and to a lesser extent, the numbers 1 through 31. You also want to avoid numbers that form a pattern on a lottery ticket, and I once read where even numbers are picked more often than odd numbers.

[ncray]

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Please. Your friend is wrong. If you flip a coin, get heads and flip it again, everybody knows you're more likely to get heads.


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I meant a fair coin.

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If you had read the paper you would know it refers to a fair coin. To sum it up, if you try flipping a fair coin as fair (vigorously) as possible, it's about 51% to come up the way it started.