Talk:Gambler's ruin

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This makes absolutely no sense:

For example, the rare happening of a coin flip to be heads a dozen times in a row is a gambler's ruin, because it's intuitively well outside the odds, but in reality it's just as likely as any other specific combination of heads or tails.

A coin flip being heads a dozen times in a row is highly unlikely. It is not just as likely as any other combination of heads or tails. Half heads and half tails is the most likely combination, according to statistics.

- Anonymous

The piece quoted makes perfect sense (though perhaps it should be reworded); you misunderstood it. It is true that a dozen coin flips coming up all heads is highly unlikely. However the sequence HHHHHHTTTTTT is exactly as likely, as is a more reasonable-looking sequence like HHTTTHTHHTHH. However, there are many, many sequences that allow six heads and six tails, and only one that allows a dozen heads, so of course you're right that a half-dozen heads total is far more likely than a dozen heads total, but the quoted piece in question was discussing individual sequences. The point is that it only happens that 1 time in N, but it will still happen eventually and everything else being equal the tendency will be for the player with the lesser bankroll to lose, when such an improbable sequence clears out his bankroll, whereas the player with the greater bankroll can handle the fluctuations better. See? - furrykef (Talk at me) 17:06, 7 Jan 2005 (UTC)

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Cigor:

Casino has:

• much more pennies than any participant;

Yes, but as noted above, this does not help them get ahead in the long run. They also have to be careful with very high rollers, since the ratio of bankrolls is not so overwhelming, so the probability of a very high roller breaking the casino is non trivial.

• odds that are skewed in their favor;

This is where they make their profit. 5% house edge (e.g. US roulette) means 5% gross profit before taxes, overheads, etc. There is no extra gross profit resulting from the bankroll ratios or other factors. Against reasonable blackjack players, their edge can be less than 1%. Against some clueless blackjack players, it might be over 20%.

• various risk management techniques that limits their maximum loss;

As noted above, they have to be cautious with very rich patrons.

The combination of above allow casino to come ahead in the long run. For a illustration see this Gambler's Ruin simulation [1]

I don't see how this link supports your argument. --Mike Van Emmerik 22:41, 17 October 2005 (UTC)

Mike,

I understand and agree with what you are saying, but I am not convinced why my text needs to be deleted. I never claim that high probability of failure is equivalent to negative expected outcome. However, even with unbiased coin and zero expected reward, 99% failure rate is 99% failure rate even with 100 fold reward. It means that the vast majority will fail even in fair circumstances, and I think this is the essence of Gambler's ruin.

As for the link, if you scroll to the bottom there is neat applet simulator where you set probabilities, and starting capital and generates one sequence of outcome based on that. I thought this was pretty educational.

So unless you give me stronger reasons, I will revert my changes, at least part of it.--Cigor 00:46, 18 October 2005 (UTC)

OK, no problems as long as you make it clear that the bankroll ratio does not affect expected return. That's what I perceived, and what I objected to. Oh, and "many more pennies" rather than "much more pennies" please :-) --Mike Van Emmerik 11:43, 18 October 2005 (UTC)

How about now? --Cigor 14:31, 18 October 2005 (UTC)

OK, good, though you'll see I could not resist a few edits for clarity. I've only just noticed that this casino related discussion possibly should be integrated more with the next section, titled "Casino games". I'll leave that for someone else. --Mike Van Emmerik 21:48, 18 October 2005 (UTC)

[edit] Huh?

None of the lead on this piece matches at all what I understand as the Gambler's Ruin, as that term is used mathematically. Did I miss something entirely?

As I understood it, the lead ought to look something like:

The Gambler's Ruin is a reasonably complex theory of statistics which, succinctly stated, says that if you gamble long enough, you will always lose, because the the distribution of random numbers cannot be predicted, and therefore losses will eventually outnumber both wins and the chooser's 'bankroll' (whether that be money in an actual game, or a mathematical equivalent).

I don't see anything in there anything like that. Is that not even close, and I'm a mathematical clod? --Baylink 22:06, 23 March 2006 (UTC)

I think the treatment here is best:

Eric W. Weisstein. "Gambler's Ruin." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GamblersRuin.html

So the main point is: even with fair odds (50% chance of either player winning each individual wager), the player with the greatest bankroll has the greatest chance of ruining the other player in the long term, in the hopefully artificial but interesting case of repeated play until one player is ruined. Having a house edge and (usually!) the greatest bankroll merely accelerates this process for the casino.

I was never really happy with this article, either. --Mike Van Emmerik 23:19, 23 March 2006 (UTC)