# Of Black Swans and Black Jacks

#### StandardDeviant

##### Well-Known Member
So there I was...facing a rainy Sunday and a long list of honey do's. There was only one way out. Crank up CVCX and claim that I was busy doing "work."

I decided to use CVCX to help me get a better understanding of life in the short run. After all, we always talk about EV in the long run, but as John Maynard Keynes put it, "In the long run we are all dead." While I'm not 100% sure, I'm gonna bet that trying to play while dead is harder to do than sneaking back in to play after being backed off at one of the downtown joints for spreading 1:8 on SD.

When I run sims with CVData, the software tells me to not trust results of less than 200 million hands. Let's see, 200 million hands is about 2 million hours of play, or about 1000 years if I could somehow manage to play 2000 hours a year (which I can't). I guess Keynes was right.

I wanted to understand what to expect for a shorter period of play, say up to 5000 hours. This is closer to what I might be able to muster over the next 10 years or so.

So I set up CVCX to model a sample game condition and tell me the results of 100, 200, 300, ... 4900, 5000 hours of play. I looked at EV, +/-3SD, and the probability that my results would be > \$0. The attached graph shows the highlights.

Summary of Results
1. EV increase linearly as playing hours increase - as expected
2. The maximum risk of loss occurs at about 1,100 hours
3. Risk of a negative result is pretty low after about 1,300 hours (i.e., a -2SD outcome)
4. Risk of a negative result declines to nil after about 3,600 (where "nil" is defined as a >3SD outcome)

This little exercise was intersting but somewhat unrealistic because it assumed that the minimum bet remained constant even as bankroll increased. Most players would chose to play at higher stakes as they progress in earnings.

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#### blackjack avenger

##### Well-Known Member
A Sigh of Releif!

Number 2 was interesting. So many can expect the potential for maximal loss to occur during the length of many players careers! I find that comforting!:joker::whip:

Number 3:
So at some point beyond the length of many careers is when the risk of a negative result get's pretty low. Again, comforting!:joker::whip: For the player who plays 10 hrs a month they will reach this number in 30 yrs. I feel quite releived!:joker::whip:

If one resizes their bets based on bankroll fluctuations then these short & long run numbers become greatly magnified!:joker::whip:

#### StandardDeviant

##### Well-Known Member
blackjack avenger said:
Number 2 was interesting. So many can expect the potential for maximal loss to occur during the length of many players careers! I find that comforting!:joker::whip:
If you look at the area of the -3 SD curve under the X axis, and compare that with the area of the corresponding +3 SD curve above the X axis, you see that there is much more area under the latter. This means that, while it is possible to end up with a loss after playing 1,100 hours, it is much more likely to end up with a significant gain. Success is likely, but it is not guaranteed.

Also, keep in mind that I've drawn the third standard deviation lines here (3 SD). 3 SD events happen only (1 - .997) percent of the time. So out of 1,000 only 3 can expect to experience the "maximum loss" at 1,100 hours.

Most of us can expect to be somewhere near the straight EV line, but a few unlucky souls will find themselves in negative territory.:cry:

#### blackjack avenger

##### Well-Known Member

I agree with you to 3SD's

However!:joker::whip:

I was linking length of potential career to the numbers you provided. It's more horrific then probably many realize.

At 1,000+ hours it's also a problem if you are breaking even or are not winning enough!:joker::whip: In the real world you would have expenses regardless of if you consider them with your bankroll or separately funded.:joker::whip:

So many at the 1,000+ hour mark will be disappointed and not just those facing max loss potential. Those that are losing, those that are breaking even, and those that are winning marginally will be :cry::joker::whip:.

#### bj21abc

##### Well-Known Member
Noticed that the game simmed was 6D s17 DAS Sr (presume this is late surrender ?) 67% pen 1-10 ramp. A 6D game with 2 decks cut off limited to a 1-10 ramp is really not a great game... (play all I presume?)

If we were to run the same exercise with better pen, or fewer decks, better ramp... I am betting we should see quite a shift in the numbers.

D.

#### StandardDeviant

##### Well-Known Member
bj21abc said:
Noticed that the game simmed was 6D s17 DAS Sr (presume this is late surrender ?) 67% pen 1-10 ramp. A 6D game with 2 decks cut off limited to a 1-10 ramp is really not a great game... (play all I presume?)

If we were to run the same exercise with better pen, or fewer decks, better ramp... I am betting we should see quite a shift in the numbers.
Yes. Play all in this simulation. I wanted to create somewhat of a "worst case" scenario. Most situations would be better than this one.

#### blackjack avenger

##### Well-Known Member
Not So Innocent

StandardDeviant said:
Most players would chose to play at higher stakes as they progress in earnings.
This innocent little statement is full of sin!:joker::whip:

If you resize frequently the long run numbers go up about 4 fold!:joker::whip:

So even with a better game if you take into consideration resizing your bank the long run is staggering!:joker::whip:

#### nottooshabby

##### Well-Known Member
StandardDeviant said:
If you look at the area of the -3 SD curve under the X axis, and compare that with the area of the corresponding +3 SD curve above the X axis, you see that there is much more area under the latter. This means that, while it is possible to end up with a loss after playing 1,100 hours, it is much more likely to end up with a significant gain. Success is likely, but it is not guaranteed.

Also, keep in mind that I've drawn the third standard deviation lines here (3 SD). 3 SD events happen only (1 - .997) percent of the time. So out of 1,000 only 3 can expect to experience the "maximum loss" at 1,100 hours.

Most of us can expect to be somewhere near the straight EV line, but a few unlucky souls will find themselves in negative territory.:cry:
Standard Deviant,

Wouldn't only 1.5 out of 1000 expect to experience the "maximum loss" at 1,100 hours? I thought that 3SD's will encompass 99.7% of all possible outcomes, with the remaining 0.3% divided evenly between the two extremes of the curve. So 0.15% would experience the "maximum loss" (-3SD) at the left end of the curve while those fortunate few at the right end of the curve would experience the "maximum gain" (ie. +3SD)?

nottooshabby

#### StandardDeviant

##### Well-Known Member
nottooshabby said:
Standard Deviant,

Wouldn't only 1.5 out of 1000 expect to experience the "maximum loss" at 1,100 hours? I thought that 3SD's will encompass 99.7% of all possible outcomes, with the remaining 0.3% divided evenly between the two extremes of the curve. So 0.15% would experience the "maximum loss" (-3SD) at the left end of the curve while those fortunate few at the right end of the curve would experience the "maximum gain" (ie. +3SD)?
You are correct. I forgot to divide the probability outside the 3SD lines by 2 to account for just the negative half. Thanks NTS. While I'm correcting things, I should point out that the first column in the table is labeled "hands" while it should read "hours."

#### StandardDeviant

##### Well-Known Member
Why it's called gambling

blackjack avenger said:
This innocent little statement is full of sin!
If you resize frequently the long run numbers go up about 4 fold! So even with a better game if you take into consideration resizing your bank the long run is staggering!
Excellent point, BJA! The 3SD curves would widen with each corresponding jump in minimum bet. I wonder if the lower 3SD curve would ever get above the X axis if the bets continue to increase.

I think I'll rerun the sim with jumps in minimum bet size when the bank roll grows to 100 time the maximum bet, i.e., at 10K, 15K, 20K, etc.

#### blackjack avenger

##### Well-Known Member
Gambling it is!

For fixed bets the 3sd long run is 9NO
For kelly bets the 3sd long run is 36NO

If you resize at all the long run NO is closer to the kelly NO number.

Throw in human imperfection and expenses and it's humorous:joker::whip:

#### StandardDeviant

##### Well-Known Member
blackjack avenger said:
For fixed bets the 3sd long run is 9NO
For kelly bets the 3sd long run is 36NO

If you resize at all the long run NO is closer to the kelly NO number.

Throw in human imperfection and expenses and it's humorous:joker::whip:
I was thinking about N0 while I was cranking the sim and wanted to look at long run in terms of N0. I have a conceptual understanding of N0 but would like to learn more. Can anyone point me to good articles or posts? Thanks in advance, and good luck at the tables. Apparently we'll all need it.

#### 10JQKA

##### Member
I only just stumbled upon this thread, it is indeed very interesting.

One thing I would find quite interesting are where abouts are the 1SD and 2SD on that graph.

Also you stated the (poor ) game and the bet size and spread but you did not state the bankroll, or I missed it.

#### sagefr0g

##### Well-Known Member
StandardDeviant said:
I was thinking about N0 while I was cranking the sim and wanted to look at long run in terms of N0. I have a conceptual understanding of N0 but would like to learn more. Can anyone point me to good articles or posts? Thanks in advance, and good luck at the tables. Apparently we'll all need it.
i missed reading this thread as well, seems interesting, i'll have to try and understand it, lol.

here are a few links on N0

http://www.bjmath.com/bjmath/Betsize/theory.htm (Archive copy)

http://www.bjmath.com/bjmath/refer/N0.htm (Archive copy)

probably more in this site:
http://www.bjmath.com/index.html (Archive copy)