How many hands does it take before advantage play provides a cumulative advantage?

If I get to Vegas twice a year, I'm happy. I play for four days, not constantly, but for most of the day. It dawned on me that the relatively small number of hands I do play hardly provides a big enough sample for variance to achieve a fair reflection of my advantage. In short, I'm probably no different from the guy sitting next to me with a laminated card dictating basic strategy. It all comes down to luck when you play for a few days. 

PS After four days, I was down about $700 at a $15 minimum table downtown. In about ten minutes at the craps table, I made it all up and more betting the pass and come lines and taking 4X odds. 

I don't know, but I am not sure that people can play enough hands in their lifetime to get a predicted cumulative advantage. And it would depend on the game rules, counting, betting, and strategy used.

Phil

Based on rules, penetration and use of CVCX software, the equation is referred to as NO. 

N0 is the number of hands it takes for your theoretical cumulative winnings to equal one Standard Deviation. 

N0 equals the  single hand Variance (square of the Standard Deviation) divided by the square of the single handed EV  (win rate). 

N0= Variance/EV^2

For a single handed standard deviation = 1.16, the Variance  is (1.16)^2 = 1.3456

Assuming your game, pen, bet spread etc. has an EV = 0.7%  (0.007)

N0  = 1.3456 / (0.007^2)  = 27,461.22  hands

At 100 hands per hour, it would take about 275 hours to reach N0. If you want to know how many hands it would take to surpass 2  standard deviations, just multiply the Standard Deviation by two (2 x 1.16) and rerun the calculation.

If  someone sees an error here, please correct me.

One error. The SD, and therefore the variance, is much greater than your numbers, which are for BS flat betting. When you spread, you greatly increase these numbers.

See chapter 10 of BJA3 for some of the values.

And, of course, you stated it correctly, but it may be easier to just observe that 2 NO is four times 1 NO, while three NO would be nine times.

Don

Thanks for the feedback Don. Chapter 10 is the gift that keeps on giving. 

OP  - For a 2D, H17, DAS dealt 70/104 and a 1-8 spread, the EV is 1.26% and the SD/hand is 3.23.  This gives an N0 of 65,715  hands.

Hmm, that N0 seems too high to me. Under similar conditions, meaning 2D, H17, DAS, 70/104, 1-8 spread, but using CAC2 with 22 indices (R22), I get an N0 of 14679 corresponding to a SCORE of 68.13.

Sincerely,

Cac

The N0 does seem high, but maybe that's because the 3.23 SD is high? I took the W/L % and SD/hand from Table 10.59 in BJA2. Those sims used the I18 indices. 

I travel with my paperback copy of BJA2 while my hardcover BJA3 stays at home, so maybe those figures have been updated in BJA3?.  

From BJA3

Table 10.94 of Chapter 10 gives for the 1-8 Optimal NO=17986 and for Practical NO=18227 with corresponding EVs of 1.47% and 2.05%

Is the overall standard deviation per hand for each bet spread listed in BJA3 chapter 10 tables? I see the standard deviation per hand in units for each true count level and the % each true count occurs, and I also see the standard deviation per 100 hands but was looking for the  overall standard deviation per hand. Thanks.

Phil

As SD is a square-root function, if you have the SD for 100 hands, then the SD for a single hand is one-tenth of the 100-hand value.

You know that there's a paperback version of BJA3, right? And, it has a lot more information than the hardcover, which was the first edition. We're up to the third edition now. Worth the investment.

Thanks Don. Ordered!!!

Thank you, yes, I have the 3rd edition (2005) in paperback. In table 10.94 (2d h17 das PA pract. 1-8) on page 263 the SD/100 hands is $697.72. One tenth is $69.772, with a $20 unit the SD units per hand is 3.4886. The EV% is 1.26. 

So would NO be (3.4486^2)/(.0126^2 ) or 12.1703/.00015876 ?

I am geting an NO of 77,658, the book has NO of 18,227. I am not sure where my error is, is it the EV or SD units?

Phil

You can calculate N0 as 10000*100/SCORE = 1000000/SCORE = 1000000/54.86 = 18228

Sincerely,

Cac

Or, N0 = 69.772² / 51.68² * 10000 = 18227

Sincerely,

Cac

You can't use the EV as a percent. You have to use units, just like the SD.

Don

Ok, thanks, it is 12.1703/(.5168/20)^2) for N0 of 18,227

Phil

Actually, you could avoid using the unit ($20). Simply: N0 = 69.772^2/0.5168^2

Sincerely,

Cac

In chapter 10, what basic strategies are used for 1, 2, 6 and 8 decks? I see the basic strategies in appendix B of the book, wasn't sure what was used for the simulations in chapter 10 though.

Phil

Not sure how to answer. There's only one correct BS for any game and rules set. We used whatever was correct.

Don