New iOS app shows real-time EVs as you play

[Three]

I really like the way you get the deck composition bar graph and the TC (RC and decks yet to be played) and the actual advantage all up at the same time that the deck composition is up. You can see how all ranks are represented for each actual advantage.

What is the -0.001 below the player advantage?

You could incorporate an optimal betting ramp suggestion for bet size based on the actual advantage rather than TC estimation of advantage. You seem like you might need some teaching on the money management part of the game. There is a proper balance between risk and reward by scaling bets to to the size of your advantage. The sweet spot between risk and increased advantage bet size increases is determined by your risk of losing your BR and the size of your bankroll. You will have little trouble getting help here to speed up the learning curve.

An app like that would be great. You could see the optimal bets for both for your count's estimated advantage and the advantage for the particular deck composition represented in the rank bar graph.

I recommend an option to the bar graph representation for either shows actual ranks (as you did) or by card value were the 10-K are all listed as one bar, "T", instead of individually because they are all ten value cards.

It looks like you are on the right track. THe software guys may be willing to help you achieve or make sure you have sufficient accuracy to all the values displayed. I guess that is a trade off between accuracy and speed. That could have optional settings as well. Some people may just want to be able to simulate play fast and others may be more interested in slower, more accurate displays. Most people would probably find uses for the extreme settings on both ends of that equation. Whether they are practicing quick decision making or ingesting all the potential info on the screen.

I bet Tarzan will love this device. You might do well to let him test its potential for using the extra information on the display.

People would want to be able to change the rules, number of decks both being used in the game and behind the cut card. People might like an exact visual bar graph of the discarded cards as they accumulate set in a discard tray for deck estimation skill practice.

I think if you incorporate as much of these suggestions into your app, it will appeal to a lot of people that are serious about a blackjack training. device. As long as the accuracy was sufficient your app would be really something. People that learn quickest as a visualization will love this thing.

If it would work for any counting system or at least the most popular level 1 counts to level 2 counts, both ace reckoned counts and ace neutral counts, both balanced and unbalance counts. The appeal just reached everyone.

I thought of another really cool feature. If it allowed you to set various deck composition in the bar graph so you could see how whatever configuration you wanted was for all your outputs.

Add a digit to the TC display. People use different techniques for rounding.

[Three]

Click on Norm's BJ resources in the tool bar above and then click on CVCX online. Look at the inputs that BJ players are interested in. Look at the outputs. You might want to play with the various inputs and see how the output changes. Notice that standard error increases as frequency for an event decreases.

[tomker]

Wow, you wrote a lot of stuff. I will try to address it all. Please let me know if I forget something.

The -0.001 is in the row for "fresh deck" EVs. So in the case of the "bet" button that's the house advantage of the game, overall. By default my app has very liberal rules, as you can tell.

You're right, nothing about the app addresses money management yet. I will put that on my to-do list and post about it if/when it happens.

My first instinct was to group all the tens together on my graph but that either makes the graph look stupid because one bar is 4 times taller than the others, and it's impossible to eyeball the deck composition, or of I divide its height by 4 to normalize it, you again can't eyeball the graph to see how many tens there are because they have 1/4 of the visual weight. So displaying each card individually gives you a much better idea of deck composition at a glance.

If somebody wants to check the accuracy of my numbers then nothing is stopping them. I am not too concerned about it though. If you look at one of my previous posts, I explain how I have two different bodies of code that are able to calculate EVs using completely different methods, and to test and debug them I make sure they agree with each other. And right now they do, so I have a high degree of confidence that my numbers are accurate.

There's not really a trade-off between speed and accuracy. Simulating more hands will give you better results, so you always want the simulation to run as fast as possible. You might be referring to which pseudo-random number generator (PRNG) is used... better PRNGs often run slower and you might consider their output more "accurate." But I tested Apple's default PRNG vs. a nice cryptographic one and couldn't measure any difference in the accuracy of my MC simulations and Apple's one is 3 times faster, so I use that.

I don't know who Tarzan is (I assume a forum member?) or how to get in touch with him. If he wants to download the app then he's welcome to, as is anyone else.

The app already lets you change the rules and deck penetration. The graph of "revealed cards" that I showed in the screen shot (linked above) will effectively show the contents of the discard tray if you look at it between hands.

I will put your ideas re: specifying deck composition and displaying the TC with more accuracy on my to-do list also.

By the way, please don't take this the wrong way, because I'm happy to discuss the app, but you seem to be asking a lot about features the app already has and suggesting a lot of features that the app already has. A lot of this could be sorted out if you just downloaded the app. It only costs $6. I don't really understand your reluctance to do so. If you don't have an iOS device then surely you know somebody who does and who would let you borrow the device for a few minutes/hours so you could check out this app that you're clearly interested in?

[Norm]

On RNG's. I have never heard of a compiler or spreadsheet built-in RNG that was usable. Indeed, nearly all are LCGs and famously horrible. But, they do cause extremely fast convergence, due to their short periods and non-randomness.

[tomker]

On RNG's. I have never heard of a compiler or spreadsheet built-in RNG that was usable. Indeed, nearly all are LCGs and famously horrible. But, they do cause extremely fast convergence, due to their short periods and non-randomness.

I'm sure a lot of built-in PRNGs are still LCGs but the one in the GNU C runtime isn't. Its PRNG does the LCG operation 3 times and shifts and ORs the middle-order bits together to create the result/next seed. This actually seems to make it pretty good (and fast) according to my tests.

Plus, if a particular PRNG makes your simulation results converge faster on the correct answer, wouldn't that be a feature instead of a disadvantage? *smiley*

[Norm]

Plus, if a particular PRNG makes your simulation results converge faster on the correct answer, wouldn't that be a feature instead of a disadvantage?

That sentence is contradictory. There is only one correct convergence rate, which depends on the variance. If it converges more quickly, it is less accurate.

[bigplayer]

I don't see how I could take it a wrong way. I am happy to learn new things. I admit that my education is in electrical engineering and we only had to take one semester of statistics at my university, which I only barely remember. So this article, or at least how it applies to determining the convergence rate of Monte Carlo simulations, has unfortunately gone over my head.

Yet you've written software that requires a decent understanding of statistics in order to properly model the game of blackjack and are, in my view, excessively defensive, when some of the games top theoreticians are critical of your methods. Do you get where the inconsistency is in this?

[tomker]

That sentence is contradictory. There is only one correct convergence rate, which depends on the variance. If it converges more quickly, it is less accurate.

Sorry Norm, I was trying to make a programming joke which I hoped was clear with my "smiley." Of course I wasn't being serious.

Although in all seriousness there have been some papers written on speeding up Monte Carlo convergence using representative samples and/or low discrepancy sampling. You can read about some of that here:

http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method

Although I'm dubious that this would be effective for blackjack.

On a related note, I've thought a little about PRNGs for MC simulation of blackjack and of course it's better to use a better PRNG but I think it's a case of quickly diminishing returns. For MC simulations of many things, each iteration requires a fixed number of random numbers, so if you catch a very low cycle and it's a multiple of the random numbers required per iteration, your simulation could fairly easily get caught in a loop where it just keeps simulating the same exact sequence over and over. But with blackjack, hands require variable numbers of random numbers and that's often dependent on the previous RNs, so I think that even if you're using an RNG with a short cycle it doesn't necessarily mean you will get bad results.

I do think you need good randomness in your low order bits though if there's a direct correlation between your random numbers and the cards you pick... obviously it wouldn't do to pick 5s more than 4s or whatever. The low order bits from standard LCGs are usually pretty bad so I'm sure it's a good idea to stay away from those.

I'm not going to switch to a lower quality RNG just to try out these hypotheses though, but if somebody else told me that their MC simulations of blackjack gave good results with a crappy PRNG I would not be too surprised.

[tomker]

Yet you've written software that requires a decent understanding of statistics in order to properly model the game of blackjack and are, in my view, excessively defensive, when some of the games top theoreticians are critical of your methods. Do you get where the inconsistency is in this?

No, I don't "get" the inconsistency because I completely disagree with your premise. You don't need to know anything about statistics to simulate blackjack hands and average the results. And you don't need to know anything about statistics to see if your results are any good.

As a proof by induction, let's consider tossing a coin. The probability of tossing a head is very obviously 0.5. Now, as long as you know how to divide, you can toss a coin X number of times, figure out the average, and eyeball your average to see how close it is to 0.5.

I have written a quick program to simulate tossing a coin 100k times, in a loop. Here are some lines of output:

average coin toss value: 0.499570
average coin toss value: 0.502760
average coin toss value: 0.502410
average coin toss value: 0.497520
average coin toss value: 0.500420
average coin toss value: 0.502530
average coin toss value: 0.498850
average coin toss value: 0.498970
average coin toss value: 0.498960
average coin toss value: 0.500180

So, as you can see very quickly, and without any knowledge of statistics, the result is (let's say almost) always within 2 decimal places of what you know to be correct.

Now, what statistics will be able to tell you is, what is the probability of your result being within a certain range of accuracy? This is valuable and interesting if you're writing a scientific paper about something, or you have to legally guarantee the accuracy of a calculation. But in the case of an iOS app that calculates blackjack odds, I would argue that it has minimal practical value over a human being simply eyeballing the numbers and saying "hey, these numbers always seem to be correct to at least 2 digits."

[Norm]

Please realize that the statements that you don't need to know anything about statistics to sim blackjack and you don't need to know anything about statistics to see if your results are any good do not engender confidence.

Take the results in your post. Now, subtract .5 from each, take the absolute value and sort. Here is the chart you get:

badrng.png

We can see an apparent bunching of results. There is no reason for such a pattern with a simple coin-toss and 100k hands, suggesting that it is an artifact of the RNG. Of course blackjack is vastly more complex than coins tosses, making eye-balling even less meaningful.

[Norm]

Just ran the same test with a good RNG. Below are the results:

badrng2.png

No apparent bunching or pattern, at least in this simplistic test.

[bigplayer]

So, as you can see very quickly, and without any knowledge of statistics, the result is (let's say almost) always within 2 decimal places of what you know to be correct.

Except that with coin-tosses you KNOW the results are supposed to be 0.5 so when you look at a bunch of 0.49xxxx and 0.50xxxxx results you fairly confident. With blackjack you DON'T KNOW what the results are suppose to be so you cannot just eyeball the results and feel confident about them.

[Dieter]

you don't need to know anything about statistics to see if your results are any good.

As a proof by induction, let's consider tossing a coin. The probability of tossing a head is very obviously 0.5.

You absolutely do need to know some things about statistics to determine if your results are any good. The mechanics of gathering and tabulating the results isn't nearly so important as the analysis of the results.

Absolutely none of the people I toss coins with expect the results to be 50/50.* I don't even expect 50/50 in a supposedly "fair" coin toss.

Now, as long as you know how to divide, you can toss a coin X number of times, figure out the average, and eyeball your average to see how close it is to 0.5.

That's why you need to understand statistics, to determine how valid your results are.

*The people I toss coins with don't determine the results based on one toss, but based on 2 or more simultaneous (unfair) tosses. This somewhat normalizes the outcome when multiple AP's are competing.