I am ok on NO and am in tune, but thanks for the math deivation. That is very definative. M Pecks and H Porter's explanations were very helpful also, in confirming my understanding of NO. (see message 99815)
I am still struggling with the big win or the big loss situation and would appreciate more intuitive or math examples like you did for NO
Sorry, the price of crab legs is coming
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
Gamblers want to believe that if they just continue to plug away, to play a few more million hands, their dollar results will finally approach the average dollar result, that somehow (through the magic of the "long term") their previous bad luck will be compensated by a future run of good luck. But the math does not support this cherished gambling belief
....................................................................
(no "regression to the mean" with "independent events").
And in your own words, what does that mean.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
That intuitively make sense. However, past discussion reference have suggested using a risk of ruin program to show that even with a positive game you eithe win or lose, not end up in the middle. It would seem like with a positve game the chances of ending up a big loser would be very small
Crab leg prices are on the rise!
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
Here's an extreme "NO" example showing your chance of being ahead can be quite far from the 84% predicted from the normal distribution.
Consider FPDW with (gulp!) 10% cashback. Your expected win is 10.762%. Variance is still 25.84. "NO" is 2231 hands (see below).
There is more than a 93% chance you will be ahead at NO. (not 84%)
--Dunbar
It's easy to confirm that "NO" is 2231 hands:
1. The expected win after 2231 hands is 2231 * 10.762% = 240 units
2. The standard deviation after 2231 hands is SQRT(2231 * 25.84) = 240 units.So, the expected win after 2231 hands is the same as one standard deviation. That's the definition of "NO".
I got the 93% chance of being ahead at NO from DRA-VP.
I haven't followed the discussion, so I may not be using accepted
terms properly, but I assume the answer to your question lies in the
distinction between the absolute deviation from the mean and the
percentage deviation from the mean. As the number of trials
increases, the absolute deviation from the mean tends to increase and
the percentage deviation tends to decrease. Flip a coin 100 times and
the absolute deviation from the mean might be 5 or 10, which would
make the percentage deviation from the mean also 5 or 10. Flip it a
million times and the absolute deviation can easily be 1000, which is
far greater than any possible absolute deviation after 100 flips, but
would only be .1%, which, unless the result of 100 flips is exactly 50
heads and 50 tails, which is unlikely, would be far less than any
possible percentage deviation after 100 flips.
--- In vpFREE@yahoogroups.com, "cdfsrule" <cdfsrule@...> wrote:
I hope its clear to folks that just because you play longer you don't earn a higher likelihood of being closer to the mean. Quite the contrary......................................................................
That is the part that I do not understand,nor do I see how any of the discussion of NO and CLT answers that. Like I asked NOTI, I would appreciate a intuitive explanation of the above statement, as I do not see how it is so. I am not saying you are wrong, in fact you and every body else has been most helpful. Forgive me if this has been discussed before, but like I said I did not unerstand you statement abobe then, nor now. So often links to somebody's chart or curve is thrown out, but often no more words of explantion are given. I just have a hard time with that.
To the fourm members, if this is boring you, I am sorry. My next posting will be about the price of crab legs or something that I can understank
That all makes sense, but how does that explain that I am going to be either a big winner or a big lose on a positive game?
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
I haven't followed the discussion, so I may not be using accepted
terms properly, but I assume the answer to your question lies in the
distinction between the absolute deviation from the mean and the
percentage deviation from the mean. As the number of trials
increases, the absolute deviation from the mean tends to increase and
the percentage deviation tends to decrease. Flip a coin 100 times and
the absolute deviation from the mean might be 5 or 10, which would
make the percentage deviation from the mean also 5 or 10. Flip it a
million times and the absolute deviation can easily be 1000, which is
far greater than any possible absolute deviation after 100 flips, but
would only be .1%, which, unless the result of 100 flips is exactly 50
heads and 50 tails, which is unlikely, would be far less than any
possible percentage deviation after 100 flips.
I agree that it can be confusing. Bad luck won't be "compensated for"
in the long run, but, in percentage terms, while "regression to the
mean" may be a myth, results can be counted on to approach the mean as
the number of trials increases. I think the "magic of the "long
term"" is a good description of that phenomenon. To not distinguish
between percentage deviation from the mean and absolute deviation from
the mean makes clarity impossible.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
Gamblers want to believe that if they just continue to plug away, to play a few more million hands, their dollar results will finally approach the average dollar result, that somehow (through the magic of the "long term") their previous bad luck will be compensated by a future run of good luck. But the math does not support this cherished gambling belief
....................................................................
(no "regression to the mean" with "independent events").
And in your own words, what does that mean.
It depends on whether you're talking about a big percentage winner or
loser or a big absolute winner or loser. The more you play, the more
your results will approach the mean in percentage terms. Whether
that's "big" or not depends on several things. But in absolute terms,
the more you play, the more your results will deviate, both from the
mean and from break even, thus making your absolute win or loss "big."
It might not easily make sense that your loss in absolute terms if
there's a loss will be greater on a positive game as the number of
trials increases and it's probably complicated to show why that's
true, but it probably is, although I suspect that there's a number of
trials past which the average loss if there's a loss in a positive
game decreases.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
I haven't followed the discussion, so I may not be using accepted
terms properly, but I assume the answer to your question lies in the
distinction between the absolute deviation from the mean and the
percentage deviation from the mean. As the number of trials
increases, the absolute deviation from the mean tends to increase and
the percentage deviation tends to decrease. Flip a coin 100 times and
the absolute deviation from the mean might be 5 or 10, which would
make the percentage deviation from the mean also 5 or 10. Flip it a
million times and the absolute deviation can easily be 1000, which is
far greater than any possible absolute deviation after 100 flips, but
would only be .1%, which, unless the result of 100 flips is exactly 50
heads and 50 tails, which is unlikely, would be far less than any
possible percentage deviation after 100 flips.That all makes sense, but how does that explain that I am going to be either a big winner or a big lose on a positive game?
As long as you relate to the "percentage of coin in", you will get closer and closer to an "average" result, percentage-wise.
And, it is true, that when you use the "number of dollars", the differences will get very large. And, larger and larger, but slower than the average difference.
My argument is, and has always been, you must normalize. This is why a 100 point jump in the DJIA years ago was so much more important than a 1,000 point jump today. You have to deal with percentage jumps of the DJIA to do proper comparisons.
..... bl
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
I find however that most gamblers are not aware of this mathematical fact. Gamblers want to believe that if they just continue to plug away, to play a few more million hands, their dollar results will finally approach the average dollar result, that somehow (through the magic of the "long term") their previous bad luck will be compensated by a future run of good luck. But the math does not support this cherished gambling belief (no "regression to the mean" with "independent events").
In the end it's the absolute deviation (money in the pocket) that counts. Other statistics, like percentage deviation are interesting, but percentage deviation doesn't bring home the bacon.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
To not distinguish
between percentage deviation from the mean and absolute deviation from
the mean makes clarity impossible.
There is a minimum, if memory serves me, the minimum on the one SD line is at N0/4. Presumably the average loss on a positive gamble would also have, in this case a maximum point, probably in the neighborhood of N0/4. But many gamblers don't make it to that point, largely because they're playing games with unreasonable N0's.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
although I suspect that there's a number of
trials past which the average loss if there's a loss in a positive
game decreases.
In the end, yes, but that's only relevant ex post. Ex ante, what
matters is that one can have faith that one's results will tend to
approach the mean, in percentage terms, as one plays more. If the
only thing that matters is results, there's no basis on which to play.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
To not distinguish
between percentage deviation from the mean and absolute deviation from
the mean makes clarity impossible.In the end it's the absolute deviation (money in the pocket) that counts. Other statistics, like percentage deviation are interesting, but percentage deviation doesn't bring home the bacon.
Yes, the worst time to be one standard deviation below your expected return is
when you have played NO/4 hands. I posted about this maybe 10 years ago on the
old bjmath site, and I dubbed this number of hands "Nhell". (it didn't stick!)
For FPDW with no cashback, Nhell occurs at about 111,000 hands. At 500
hands/hr, you have to play 223 hrs to get past Nhell.
The worst time to be 2 standard deviations below expectation, Nhell2, is exactly
at NO hands (about 445,000 hands for FPDW). And you don't reach Nhell3 until 2.25*NO
hands, which for FPDW would be about 1.78 million hands.
--Dunbar
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@> wrote:
> although I suspect that there's a number of
> trials past which the average loss if there's a loss in a positive
> game decreases.There is a minimum, if memory serves me, the minimum on the one SD line is at N0/4. Presumably the average loss on a positive gamble would also have, in this case a maximum point, probably in the neighborhood of N0/4. But many gamblers don't make it to that point, largely because they're playing games with unreasonable N0's.
The situation is not that dire. It merely requires a readjustment of your beliefs. If you play N0 hands of a positive gamble, you can expect to be ahead about 84% of the time, or stuck in NHELL2sd about 2.5% of the time. If that's too vague, you probably should not be gambling, because, like it or not, that is the situation. If your expectation is to get within say 10% of the ER with 95% confidence, that will take a long while indeed, probably longer than you realize. Thus, that kind of expectation is unrealistic for typical gambling.
Furthur reading:
http://members.cox.net/vpfree/FAQ_LT.htm
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
If the only thing that matters is results, there's no basis on which to play.
