optrader: Chance of being ahead vs time

[optrader]

Hello, Don & Experts,

Is there a formula, website, or simple rule(s) of thumb, for determining the chance of being ahead vs time played (or # hands played)? Don's book gives an excellent discussion of Risk of Ruin and calculations for a given bank roll, edge, std dev, plus # hands played. I was just curious of the other side of the "equation" - "Risk" of Return...

I also recall some place in Uston's book that for a given edge (e.g. +1.5%, 100 hands/hr), the % chance of being ahead was 67% after 10 hrs, and 73% after 20 hrs. I don't recall whether 2d vs 6d, table rules, etc. Sorry!

Thank you for your help.

[Don Schlesinger]

You missed BJA2, p. 24 chart.

Once you know the EV and SD for a given game, these numbers can be found by consulting a cumulative normal distribution chart, which also is in the book, pp. 165-6.

You need to calculate what's known as the z-statistic.

Don

[Don Schlesinger]

I have a little time, so let me work you through an example of how one of the numbers in Table 2.2 was derived.

Let's take the 4-deck play-all game (last column). From p. 26, the EV (win rate) is exactly 2.00 units per hour (line 5) and the SD (line 9) is 31.23 units per hour.

What's the chance that we'll be ahead after 50 hours of play (assuming, by the way, that we always have enough capital to complete the 50 hours of play)?

Well, the SD for that amount of time is 31.23 x 50^.5 = 220.83, and the EV is 2 x 50 =100.

So, if we're to break even, we have to lose the 100 units we were entitled to, which represents a loss of 100/220.83 SDs, or 0.45 SDs.

From the p. 166 table, we find 0.45 and the entry is 0.6736. Back in Table 2.2, we read that the probability of being ahead (winning one cent more than break-even) is 67%.

Got it? To test yourself, just use any of the other games and see if you can reproduce the various answers in the tables.

Don

[optrader]

Don -

Thanks a bunch! Always nice to know that detailed answers (and an example in this case!) is available just around the cyber-corner!

I'll try and put in some values as per your recommendation. Thank you.

:>)