LLN Question (FGators Question)

[alThor]

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lol at thinking definitions on MathWorld are worded poorly.

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lol at thinking MathWorld is perfect. You know it isn't just Weisstein, right?

Check out the 2nd last sentence of their Gambler's ruin page. (Refers to casinos.) The way it's written, it implies that even if casinos offered favorable games, they'd still come out ahead due to their "deep pockets". I pointed this error (or at best, poor wording) out to the maintainer years ago, but it's still there.

MathWorld is a great reference, but don't worship it.

[Catyoul]

It was a misunderstanding in the first place, and I still don't think any definitions are wrong. From what I understand from the Gambler's ruin page, it didn't say that casinos would come out ahead with favorable games but equal ones :

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Even with equal odds, the longer you gamble, the greater the chance that the player starting out with the most pennies wins. Since casinos have more pennies than their individual patrons, this principle allows casinos to always come out ahead in the long run. And the common practice of playing games with odds skewed in favor of the house makes this outcome just that much quicker.

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I agree it could be worded better.

[jason1990]

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It was a misunderstanding in the first place, and I still don't think any definitions are wrong. From what I understand from the Gambler's ruin page, it didn't say that casinos would come out ahead with favorable games but equal ones :

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Even with equal odds, the longer you gamble, the greater the chance that the player starting out with the most pennies wins. Since casinos have more pennies than their individual patrons, this principle allows casinos to always come out ahead in the long run. And the common practice of playing games with odds skewed in favor of the house makes this outcome just that much quicker.

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I agree it could be worded better.

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Suppose I open a casino in my home where I offer even money coin flips at $1 a piece. I start with a $1,000,000 bankroll and every one of my customers has only a $10 bankroll. Imagine that, for some reason, I only take one customer at a time. There is a line outside and when one player busts, the next player comes in. If the supply of players waiting outside is effectively limitless, then I am effectively playing against only one opponent who has an infinite bankroll. The fact that my bankroll vastly outweighs the bankroll of each individual customer is completely irrelevant, and cannot save me from eventually going broke.

[pzhon]

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lol at thinking MathWorld is perfect. You know it isn't just Weisstein, right?

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That there are other contributors than Weisstein is the main reason it is as reliable as it is. He's not a mathematician, and has little direct contact with most of the areas covered by MathWorld.

Early in its history, he asked me to take over or take some sort of leading role, and I declined since fixing the errors looked like too much work. It has gotten a lot better.