Has anyone published the following...

Given that the only way to win over the long run is to own a casino, the only way to win is to "win over the short run". Most folks follow the old adage to figure out what they can aford to lose and budget for that. In reality, IMO the key to winning is to understand what it takes for you to walk away a winner and budget for that rather than for what it takes for you to walk away a loser. Another observation - most inexperienced gamblers have unrealistic expectations and therefore are basically guaranteed to lose - as an example someone may want to win 1000$ but is only betting 1$ playing optimal blackjack or whatever. The chances of ever getting ahead 1000$ is virtually nill unless you've got an enormous bank and live in the casino.

So here's my question: has anyone published tables which give the following information:
Given a goal of winning "X" - and that once I'm ahead "X" I will walk away from the game, based upon how much I'm betting what's the chance I'll ever be ahead X amount? In plainer english and using Baccarat as an example: if I want to win 500$ and always bet on the banker - what's the chance of doing that if I bet 500$ v 100$ v 50$ v 10$ ...?

I would think such tables would be of enormous benefit for each of the major table games played with optimal strategy. The key to money management is knowing what you need to be betting in order to have a chance to reach your hoped-for target. If you know the stats ahead of time you can more realistically adjust your betting and/or your expectations.

(Note: many years ago I started to write a book on this subject and was going to contact a mathematician at a local university to create the tables, but the work was lost and I got busy doing other things. I still think this is useful information.)

Quote: DrGrrr

the only way to win is to "win over the short run".

This must be deja vu, I already said this once
today. There is no short term, only long term.
Short term is an illusion.

Quote: EvenBob

This must be deja vu, I already said this once
today. There is no short term, only long term.
Short term is an illusion.

The correct quote is "time is an illusion, lunchtime doubly so".

But to answer the poster with a question : what's your starting bank roll in the question you ask?

E.g. I want to win $X, I will flat bet $Y, but only have $Z to lose.

I want to win $200 dollars, starting with $1000, and will flat bet $20. What's the chance of getting there?

I have some answers to this somewhere, and can run it for variety of scenarios. But for a fair game, the ratio of X to Z is key: If I have $500 and want to win $100, it's 5/6ths, with a 1/6th chance of loss:

P(win target) = target win / (target win + bankroll).

Quote: EvenBob

This must be deja vu, I already said this once
today. There is no short term, only long term.
Short term is an illusion.

there is in deed a short term, in statistical term that is called variance.

Quote: andysif

there is in deed a short term, in statistical term that is called variance.

Apples and oranges.

The best way in a -EV game is to bet that amount on one shot called "maximum boldness." If you bet minimums trying to reach that same goal, the chance of you reaching it become less likely. Conversely, when you have an edge, its best to do the opposite.

This topic is discussed a little in The World's Greatest Blackjack Book.

There are risk of ruin tables that I'm sure exist for some games. They will tell you what you want to know.

Quote: DrGrrr

So here's my question: has anyone published tables which give the following information:
Given a goal of winning "X" - and that once I'm ahead "X" I will walk away from the game, based upon how much I'm betting what's the chance I'll ever be ahead X amount? In plainer english and using Baccarat as an example: if I want to win 500$ and always bet on the banker - what's the chance of doing that if I bet 500$ v 100$ v 50$ v 10$ ...?

You can't really specify a probability unless you also include conditions under which you are forced to stop before reaching +X. Martingale systems "work" under the assumption that you're willing to risk everything you own if it comes down to it.

If the "stop condition" is a money one (e.g. you will play until you are ahead X or behind 2X), I have found that the probability of reaching +X before reaching -2X is fairly constant for a particular game regardless of how much you bet. (In other words, if you play a game with zero house edge and you bet X at a time, the probability is 2/3 that you will get to +X before -2X; if you bet less than X at a time, the probability should still be around 2/3.)

(Oh, and pardon me for being in pedantic mode today, but dollar signs go before the numbers - "500 dollars" is $500, not 500$.)

x win before 2x loss is 2/3 only for a fair game (see equation I gave earlier).

It's less than 2/3 for an unfair game, and bet size will be factor. I wish I had the spreadsheets I set up to test for this here, but I don't.

If win target is small compared to bankroll, and the game has multiple payouts (like VP), X can be reached a lot of the time. For JoB, a $10 win on a $500 bank roll playing $5 per hand is in the lower 90% of session wins. However, 90% session wins is not enough to cancel out the times when you lose it all (even ignoring the fact you are often win more than $10).

Yes, frequent readers of these pages will know EXACTLY why I was running those numbers...