Talk:Proebsting's paradox

Too limited exploration of the paradox

Thorp's case which leads to bankruptcy seems to be a very odd situation. As the bettor continues to take the bets, his expectation is increasing super-exponentially. This means that not only are his expected returns infinite, but also his expected log wealth is also rising (linearly, to infinity). So it seems that Kelly isn't the optimal case if there is a possible change in odds, but it is still better than not betting. At any stage an investor can "get off the ride" and be glad that he bet. Does anyone know of a peer-reviewed article that makes these points? --Dilaudid (talk) 16:58, 8 June 2010 (UTC)

I think that the issue here is that the discussion of the paradox relates to Thorp's analysis, of it - which would be authoritative in and of itself, given Thorp's reputation. However, the relative recentness of the analysis (2008) would seem to suggest that the amount of literature directly available on the subject would be limited. On the other hand, there might be some other relevant examples that could be applicable - perhaps from the domain of venture capital. Considering the case of a technology company that starts out with a few thousand dollars of the founders assets, working out of a garage. After starting a web site, the founders begin to get customers for the product, providing an apparent upside to the payoff - perhaps initially hoping to buy some merchandise and sell it on eBay, or to develop a software product, or maybe produce a small budget movie. In order to mirror the conditions of the paradox, the wager has to offer or appear to offer an ever increasing payoff ratio as a consequence of the bettor putting more into the project. Maybe a movie would be a good example, some small budget movies like Bliar Witch Project have gone on to make hundreds of millions of dollars, although usually not for their original creators, who usually end up selling their interets in it, that is to say as the appparent payoff increases as the project progresses - even if the payoff never really does become infinite.
Yeah, so I'm sure that someone has looked at it in some variation of a practical application. But the question would still be as to whether or not there is any citable literature, insofar as it relates to Thorp, etc., that is to say for as far as the requested content being both on-topic for this article, and encyclopedic. 71.138.131.175 (talk) 11:47, 13 October 2011 (UTC)

Another paradox which doesn't exist

Kelly works with known probability and edge, so changing odds is inapplicaple subject here. Just because Kelly is widely used in live, non-predictable environment, doesn't mean it should be applied there and even more to proclaim it's result in such an environment as 'paradoxal'.

Anyway, if one insists in using Kelly in such cases, the solution is to use the last odds offered and make adjustment accordingly. E.g. initially one being offered 2 to 1 payout and bets 25%. The payout on new bets changes to 5 to 1, so the bet should be 40%. The player simply add extra 15% of the original wealth. The substraction should be used whith lowering odds.

Just as with other similar modern 'paradoxes', it is about simple logic. No need for math theorems and advanced debates. — Preceding unsigned comment added by Activeco (talk • contribs) 16:22, 2 May 2014 (UTC)

It exists. See paradox. --2607:FEA8:F8E1:1400:B049:38D1:E13A:CF54 (talk) 15:37, 25 October 2024 (UTC)

Sources?

"Todd Proebsting emailed Ed Thorp asking about this." is a funny thing to read without any sources Dumblejosh (talk) 13:16, 18 October 2024 (UTC)