Simulator results update

In the simulator https://www.blackjack-hack.com/blackjack-hack.php I added the maximum $s at risk to the simulation results. (see "Your maximum risk ...," in the bold faced results list on the right). I also added the projected number of hands needed to be played for an approximately 84% chance for positive winnings (greater than $0). Multiply this number by 4 to get the projected number of hands needed for an approximately 97% chance of positive winnings. If the simulation is not profitable then a NULL result is shown for the number of hands.

This is to show the amount of money at risk and the length of play required for profits. Changing betting amounts, counting strategy and playing strategy can improve results.

Thank you,

Phil

Hi, Long time no see! I’ve tried the part you describe above. The simulation result shows these words: 

“You need to play 733,993 hands for an 84% chance of being in the black

Bring $1,610 to each visit to not go bust 97% of visits.”

What do you mean by “in the black?” It looks like you mean "for positive winnings." Also, I don’t understand why you specifically choose these two numbers, 84% and 97%.

Well, you may have hidden your identity for a long time on these boards, but you can't hide your (very young!) age, which we all knew anyway. Anyone who doesn't know what "in the black" means can't be much older than, well, my grandchildren!

As for 84% and 97%, they are approximately the area under the curve to the left of one and two standard deviations (z-statistics) on the cumulative normal curve.

Don

Hey there Aceside!

I thought I might be showing my age with that term. 

In the black - above 0 

In the red    - below 0

- The 84% and 97% are approximately what may happen within 1 standard deviation or 2 standard deviations as Don pointed out. 

- To converge on a number for how many hands you need to play for an 84% chance of being in the black you likely need to run many millions of hands. 

- The amount needed to not go bust during 97% of visits is the amount needed or to have available for each casino visit to not go broke in 97% of the visits. The number of hands per casino visit is set as the user would like (above the green run simulation button). A simulation run typically consists of many visits but can be set by the user.

- The maximum risk in the first bold faced output shows the worst down swing at any point during the simulation runs. This is to show the worst case $ scenario of the simulation runs.

Thanks, 

Phil

I’ve tried the simulator a few more times but am still confused about this part.  When you say “the maximum risk shows the worst down swing at any point during the simulation runs,” do you mean the maximum money drop during the continuous losing sessions?  Within each session, there are always up and down hands all the time. 

So for example if during the entire run if the simulation was never down but got up to $100k ahead and then dropped to $40k ahead and then went back up and finished. - the worst down swing in the run would be a drop of $60k even though it was never down at anytime.

I guess my question above wasn’t clear enough.  Let me ask this again using this specific figure as an example. How do you measure the maximum risk of $16,000 from this result figure?

It might be one of the slight down legs, maybe the one toward the end that looks like it went from almost $260k down toward $240k. I can add something that displays what hands the maximum down swing happens on. 

For now if you cursor along this curve on the simulation results screen it should display the amounts and hand numbers.

Also, the bold faced output with maximum risk is the maximum down swing from any of the simulation runs you have done. All the runs are combined and totaled and worst, best and averages are tracked. So if you did multiple runs the $16k could be from a previous run and the curve could be from the current run.

The maximum risk is displayed for the current run and for all the runs on the line above it labeled "Worst Down Swing" (not in bold). Maybe I should rename these to be consistent.

If you reset totals and averages or you give the results a different name (below green button) all the numbers start over.

I started to get what you mean.  Basically, you record the peak-to-trough drop that has been fully recovered. Thank you for your patience! 

In the securities industry, be it a hedge fund, a trading system--anything in which there are fluctuations in investment capital--this is commonly referred to as "maximum drawdown," and any period can be specified. Think of it this way: Suppose you were unfortunate enough to begin your investment at the peak of the beginning of the worst drawdown on the graph. How much money would you have lost?

The number is relevant in guiding people to understand that, although there is a clearcut upward trend to their investment, shit happens! And when it does, you need to have enough bank to withstand the inevitable swings.

Don

This is very relevant. From the sim figure I posted above, I find that it takes about 50,000 hands to overcome a maximum drawdown in Blackjack. This indicates that an unluckiest player may lose almost all the way down during their whole year of playing. 

Well, yes, of course. And, you may or not recall that Peter Griffin famously wrote that we are at an all-time high only about two percent of the time.

Don

I haven't looked at your simulator, so you may already have done this, but this number is known as N0 (N-zero) and you should identify it as such in your output. N0 is equally valid for negative EV situations, in which case it is the number of rounds (note that I didn't say hands, because of splitting) for the same probabilities of being in the red (hopefully aceside can figure out what that means!).

Even if it's not fully recovered, it's the worst drop during any of the runs. Thank you for trying it out!

Yes, thank you, I had it labeled as N0 at one point, I will put that reference back in. I didn't think of it equally applying to being in the red, can put that in instead of displaying NULL. Thanks.

Also down the list in the boldfaced output is "Worst down swing during a visit". This is what was the worst thing that happened during any of the simulated casino visits. (length of each visit set in the # of Hands per casino visit input)

Clearly, everybody here knows the definition of N0 better than I do.  However, I’m thinking about inventing a new terminology in Blackjack, that is, the probability of becoming a winner after 50,000 hands of playing.

Is there such a definition now?  Is it possible you add this probability to your result list? I choose this fixed number of 50,000 because this number of hands is practically possible for a player to complete within one year.

Everyone plays a different number of hands a year, and such a calculation is trivial once you know EV and SD. Just use the charts on pp. 147-148 of BJA3.

Don

You can set the # of hands per casino visit to 50,000 and run many visits and see how your strategy does. I can also look at adding something that will show the probability of being a winner with your strategy for any number hands you select. 

% of visits you leave a winner is listed in the first results section on the top right. Also the number of Visits Won and Visits Lost and is listed in the large table of results on the right when you scroll down.

With 50,000 hands per casino visit you'll have to make a lot of runs though.