I was quite excited when I saw that New Scientist - generally a pretty good magazine - had a piece on the maths of gambling. But unfortunately it turned out to be an extremely poor article.
The first three sections - on card counting, choosing unpopular lottery numbers and arbitrage - skim very briefly over well-known subject matter.
The fourth section is completely wrong - it applies the maths of a situation where you see a number of opportunities in turn until you choose one (e.g. choosing a marriage partner) to the problem of choosing when to stop gambling (where it doesn't apply at all), and draws nonsensical conclusions as a result.
The fact it was written by New Scientist's career editor is telling I suspect.
I was going to post this as an "Ask HN", but since I see someone with the username bayes writing in a probability thread- I figure why not ask here (if its all a coincidence, sorry!)
Would you happen to have a recommendation for a good probability textbook for a first year grad student?
I'm afraid my username doesn't reflect any deep knowledge of the field. I studied probability at an undergraduate level many years ago, and still use it in my hobby (writing 'bots' that run automated trading strategies on one of the sports betting exchanges here in the UK), but that's all. I'd go for an "Ask HN" thread if I were you.
I've asked this question before, and though I haven't gotten to the point where I could direct you to the best place to start, it would probably be in one of these books:
E.T. Jaynes, "Probability Theory: The Logic of Science"
Judea Pearl, "Probabilistic Reasoning in Intelligent Systems"
Ha, I searched quite hard to see if it had already been submitted, but didn't find it. Obviously I searched the wrong terms, or not for long enough. Sorry about the Dup.
Even so, the discussion at that other article was enlightening, probably more so than the article itself, so I think that submission - and sort of by proxy this one - was worth while.
Correct (although some wheels only have 0, no 00). With both, it's a 5 point something house edge. Also, the martingale (doubling) strategy falls apart with table limits, even if you have the bankroll.
I once figured out it might be possible to 'fold' a martingale so it occurs in less spins. I think the basic idea was making full use of the table limit from the first bet (eg, table limit is 100, normally you'd bet 2 to double the loss of 1, so bet 64), and making full use of the table limit 'bandwidth' before you reach the limit (possibly starting with 64 and halving thereafter to 32, 16, etc).
There is a way to test the 'advantage' of a gambling method. Take the bankroll (eg, how much money you have now, starting at 0), and the amount bet EVER (on whatever number the bets were), and divide the amount bet by the bankroll. So we've bet 100 dollars, and won 100 - the advantage is 1 (or 100 per cent).
If the advantage over 1000s of spins is < 1.3% (or 2.6%, or 5.2%), you won't beat a roulette wheel.
There´s a probability gap explained in one of those "make money" in http://en.exposedcasinos.com they say they´ve found a gap in the limits of some roulettes to make the math work. I´ve tested it and it worked at least yesterday and today. About 300 spins.
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[ 3.7 ms ] story [ 49.8 ms ] threadSo, do you know any site that aggregates bets from different bookies?
Update: http://www.betbrain.com/ is even listing SureBets :).
The first three sections - on card counting, choosing unpopular lottery numbers and arbitrage - skim very briefly over well-known subject matter.
The fourth section is completely wrong - it applies the maths of a situation where you see a number of opportunities in turn until you choose one (e.g. choosing a marriage partner) to the problem of choosing when to stop gambling (where it doesn't apply at all), and draws nonsensical conclusions as a result.
The fact it was written by New Scientist's career editor is telling I suspect.
Would you happen to have a recommendation for a good probability textbook for a first year grad student?
E.T. Jaynes, "Probability Theory: The Logic of Science"
Judea Pearl, "Probabilistic Reasoning in Intelligent Systems"
Bayesian Data Analysis, 2nd ed by Gelman et. al
Even so, the discussion at that other article was enlightening, probably more so than the article itself, so I think that submission - and sort of by proxy this one - was worth while.
Thanks for finding the reference.
If the advantage over 1000s of spins is < 1.3% (or 2.6%, or 5.2%), you won't beat a roulette wheel.