(Sorry about my careless typing.) OK, is the St. Petersburg paradox essentially that: If in a coin-matching game, I use the strategy of playing until my first win, where my bet on any given play is 2^N dollars, where N is the largest integer such that I've just lost the last N matches, (with my first bet being 2^0 = 1 dollar), so that upon each win I'm guaranteed a net profit of $1 . . . . . . then how come this doesn't guarantee me a net profit of at least $1, with probability 1, even though coin-matching would seem to be symmetrical, i.e., favoring neither player? --Dan On 2012-12-29, at 10:27 PM, Andy Latto wrote:
On Sat, Dec 29, 2012 at 2:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Is the Petersurg paradox that thing where if two people play coin toss (one player gets +1 for H, -1 for T, and vice versa for the other player), then as the number N of tosses -> oo, one might think that the most likely average score -- in terms of a probability density -- is 0, but in fact it's +-1 (i.e., the arcsin law") ???
The St. Petersburg paradox is not what you describe. The St. Petersburg paradox is when two people play a game where they flip coins until a head is flipped, and if N tails are flipped first, A pays B 2^N dollars, and the question is what B should pay A initially to make this a fair game.
I've never heard of a Petersurg paradox, and neither has any web site indexed by Google, as far as I can tell.
Andy
--Dan
On 2012-12-29, at 5:21 AM, Fred lunnon wrote:
William Feller's classic book on probability analyses the behaviour of waves --- your "regimes" --- in the sum of a sequence of coin tosses; I think the general heading is something like the "Petersburg paradox".
Presumably the sequence of CF means behaves in a similar fashion. Is the corresponding higher-order behaviour known? And how well does your data fit the known modela?
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