Optimal Non-bold play

I have seen mentioned from time to time a concept of "re-scaled" bold play that is not bold, but still optimal for the standard even money coup like craps / baccarat (i.e. "Red and Black") . I have not been able to find a clear discussion of it. The primary reference is "inequalities for stochastic processes" but that is out of print and not available. "Doctrine of Chances" (Ethier) talks about it briefly on page 328, but I don't understand when your fortune (f) reaches 1/2. Both sub-strategies say to bet zero right?

Edit: Nevermind, I misread. It is now clear that when you reach 1/2 you just bet it all.

But I won't delete the post, because maybe someone can help me understand if this has any practical use ;)
The text seems to indicate that this method will result in longer sessions with the same probability of reaching your goal.

Quote: DrEntropy

"Doctrine of Chances" (Ethier)

Edit: Nevermind, I misread. It is now clear that when you reach 1/2 you just bet it all.

But I won't delete the post, because maybe someone can help me understand if this has any practical use ;)
The text seems to indicate that this method will result in longer sessions with the same probability of reaching your goal.

Excellent text to reference to. It can also be found on Google and you can almost read the entire book.

The section you are talking about is Bold play without a house limit.

Practical use could be
On page 330 he talks about non-Bold play when "with initial fortune f=1/3"

One should know that Bold play can not be improved upon but only changed with things like house limits and high payoffs are concerned.
Either shows in a paper the only exception he knows of is betting the don't pass in craps with odds. I cant find my paper on that but I remember it was not that much of an improvement, but it was.

added: For another reading with many examples... try this pdf
How to Gamble If You Must

Quote: 7craps

How to Gamble If You Must

Actually that was where this breadcrumb trail started :)

I also know the other paper you are referring to it is something like "Improving on Bold Play in craps".

Thanks. Yes, that was the name of the paper.
I still can not find it in my collection.

When I was a Dealer in Reno last century I knew one don't bettor that came from SF and he always bought in for $1000 and bet $500 the first time.
We always asked him about it and he just said it is the best way for him to win $500 on my trip.
He did not care if he won the very first round.

Maybe he had more fun with the money in his hotel room ;)

Come to think of it, he did win the $500 way more times than he lost his $1K buy-in.
The math would agree.
I do not know if he was a long term winner. I doubt it as he never did mention it.
Us dealers just laughed at him when he left.
He was a stiff.

Ok, I finally took another look at this 'optimal non bold' strategy and discovered it really is nothing more then mathematical curiosity. It is interesting that such strategies exist, but they don't really have much practical significance, and don't appreciably extend play time.

Cheers!

removed
silly