Masquerace: Beginner's Doubt I: Calculation vs Simulation

[Masquerace]

Hi, I'm playing since a little short month only (to get an alternative to Roulette and Caribbean Stud....), I figure 50 hours total, but as I am fond of tables and calculations I studied and investigated BJ quite a bit in this time.

Just to help you size me (and your answers):
I have a degree in engineering
I was able to program in C, but last time it was over 10 yrs ago (under Win3.11...)
I remember something of statistics, so I can understand and even figure some basic combinatorial analysis offhand.
All I can commit to for my endeavours at present time tho, is what can fit inside an Excel sheet.

So.

I understood that EV, and thus BS table, could be exactly calculated with combinatorial analysis (forgive the evntually inappropriate terms, I'm not english born nor english schooled).
I stress "exactly".
I stress "calculated".
I stress "combinatorial".

Now I read on this site that many of your results rely on billion runs SIMULATIONS. Beg your pardon?

Is there something in BS that can't be exactly calculated? (I fear that Excel wouldn't do tho...).
Did I miss or overlook something?
Or maybe simulations are required to test and refine Betting Strategies based on Card Counting, while BS IS derived from exact calculations indeed?

Tell me I didn't start to build a castle on running sands... ;^)

TIA )

[Norm Wattenberger]

Yes you guessed correctly. BS can be calculated via combinatorial analysis. Card counting is a whole nuther matter. I will be quite awhile before we have the computing power to exactly calculate many aspects of counting. Take a look at the stats at the below site. We simply don't have any method of directly calculating such stats.

BJStats

[Marc]

I'm no math brain, so I simply trust the odds and sims noted on reputable sites and in reputable books and committ the strategies to memory (i.e. I play by rote.) My brains start frying when I attempt much past basic standard deviation formulas.
You, on the other hand, seem to have much better understanding of the math and the background to take advantage of AP. Which begs the question...what are you doing playing roulette and stud?

[Don Schlesinger]

> Yes you guessed correctly. BS can be
> calculated via combinatorial analysis. Card
> counting is a whole nuther matter. I will be
> quite awhile before we have the computing
> power to exactly calculate many aspects of
> counting. Take a look at the stats at the
> below site. We simply don't have any method
> of directly calculating such stats.

Also, as is being discussed on Reid's site, a precise pair-splitting algorithm is incredibly complex for CA.

Don

[Norm Wattenberger]

Yes, one has to be sure one understands the other person's definition of 'exact'

Serious Blackjack Software

[sam]

If one believes that other players' decisions have no influence on one's outcomes, doesn't it follow that a player's decision on Hand #1 would also have no influence on the outcome of Hand #2? I am considerably less of a math brain and the above is just farm boy reasoning.

Sam

> I'm no math brain, so I simply trust the
> odds and sims noted on reputable sites and
> in reputable books and committ the
> strategies to memory (i.e. I play by rote.)
> My brains start frying when I attempt much
> past basic standard deviation formulas.
> You, on the other hand, seem to have much
> better understanding of the math and the
> background to take advantage of AP. Which
> begs the question...what are you doing
> playing roulette and stud?

[Magician]

> If one believes that other players'
> decisions have no influence on one's
> outcomes, doesn't it follow that a player's
> decision on Hand #1 would also have no
> influence on the outcome of Hand #2? I am
> considerably less of a math brain and the
> above is just farm boy reasoning.

> Sam

It's not the other players' decisions per se, but the removal of another card from the deck which can influence the outcome of our hand. If we do not adjust our strategy based on this card, then we will neither gain nor lose in the long run. If we do take it into account, then it's possible to gain in the long run.

When we start considering cards in other hands, we're no longer talking about basic strategy - we're talking about card counting.

[Masquerace]

> If one believes that other players'
> decisions have no influence on one's
> outcomes, doesn't it follow that a player's
> decision on Hand #1 would also have no
> influence on the outcome of Hand #2? I am
> considerably less of a math brain and the
> above is just farm boy reasoning.

> Sam

> It's not the other players' decisions per
> se , but the removal of another card from
> the deck which can influence the outcome of
> our hand. If we do not adjust our strategy
> based on this card, then we will neither
> gain nor lose in the long run. If we do take
> it into account, then it's possible to gain
> in the long run.

> When we start considering cards in other
> hands, we're no longer talking about basic
> strategy - we're talking about card
> counting. [Magician]

Thx to all for the kind answers to a newcomer.

The two quotes actually answer to my Doubt # II ;^), and addressing them I'd say that you're both right in a way.

Having taken some rest, I'll try to clarify.

If a *different* player before me draws a 9 on his 16, and I have a 12, I might well regret that I "would have made" 21, but as that 9 is gone and I have to draw a new unknown card, my EV doesn't significantly change, except for the removal of that 9 from the shoe (and as I am forced to play with 6 decks shoes, that might be as small as 1/300th or 0.3%, depending on penetration and on count, which I do not address yet).
He decides with the goal of optimising his hand only, and I play with the goal of optimising my hand only (and I take into account the removal of the drawn cards only if I'm capable to, which I'm not, yet).

That's the solid reasoning I started from too, Sam, no different than any "farm boy" :-D

But then the seed of doubt was instilled, and I just wondered whether there "might" be any link and influnce beyond that.

Magician answered me with the very reasonable considerations that after I've drawn a card on the first box, if I consider card counting, or even just merely visible cards removal as suggested in the "Mag 7" posts, what I've *already seen* might well influence my *next* decisions.

What I was thinking of is something different tho.
I own BOTH the boxes. I might not content of optimising them *individaully and separately*.
When I take the first decision on the 1st box, I want to already take into account what would stem from it *afterwards* for my second box, to influence my 1st decision. Because I would like to have the *best TWO hands, taken into account combined together*, if I can.
IF there can be any influence from what could happen *afterwards, that is.

Imagine that you have a 15 on your 1st box and a 12 on your 2nd, against say an 8.
Individually taken you should hit both.
But just figure that you're allowed to draw one card and ONE only for your two hands together (I know, that's NOT realistic, but let's just start from there to see where my doubt stemmed from).
Of course you'd stand on the 15, as whichever the unknow card might be, you'd have less chances to bust by drawing it on the 12 [the % of a pat would stay the same, you'd just trade the chances of 3 busted hands with 3 no-points-hoping-for-a-dealer-bust].
Figure now that you're limited to draw 2 cards on your two hands togeter. That's already more complicated to figure offhand, I'll do it with Excel as soon as I find some time, but I sohuld see where I'm aiming at.

In SUMMARY:
I wanted to know whether the awareness that I want to optimize TWO consecutive hands combined together, and not just two individual unrelated ones, bears any "anticipated influence" on the 1st decision. (of course boiling down to nothing more complicated that indices, e.g. like hit 15 v 9 except if you also own a 12 after it, or if you're the last before a dealer's X and NoHoleCard...)

Norm has already answered me wisely that it might eventually be done, but it would make BS more complicated that CC itself, and as also Don pointed out, even to devise BS "a precise pair-splitting algorithm is incredibly complex for CA" (Combinatorial Analysis).
The BS calculation of which case (pair-splitting) actually also relying on simplifying assumtpions and simulations, as I understood.

[Masquerace]

> ....
> You, on the other hand, seem to have much
> better understanding of the math and the
> background to take advantage of AP. Which
> begs the question...what are you doing
> playing roulette and stud?

Oh, well, I had always thought BJ was too complicated... and indeed it's sucking up a pretty much bigger slice of my time.

After all we have mostly French Roulette in Europe (i.e. single zero), and there the House Edge is around 2.70% IIRC, not much more bleeding than the 0.55% with the BJ rules I can find available (BS only, no CC).

And anyway, the ultimate goal for me is not winning, but having fun at an affordable price.
Roulette gives you an undeniable thrill when you follow the ball spin and land, and when you happen to get an en-plein paying you 35 times the bet.
BJ is a much slower game, in both bankroll swings and emotions, as I reckon from my first, non-CC yet, experiences. It's more like a slow-buildup game.
(But I still get flustered (?) when I get a BJ which happens once in 21 on avg, I get paid a "mere" (compared to Roulette) 3/2 onto my minimal 20CHF bet, and the dealer pays me with 2 5CHF pieces, expecting a 5 tip out of 30 paid!!!!!)

Besides, you should have asked what "were" I doing... ;^)
I still sometimes enjoy some pure-luck higher-thrills roulette, and Caribbean Stud as a "cool-off" no-brainer between sessions (although the streak when I got 2 quads, 10 fulls and 6 flushes in 10 consecutive visits across Feb-March was not bad either, including for my bankroll).
But once I begun, BJ indeed took more and more of my playing time.

(BJ apart, I was going 6-8 times/year in the past, with a 4 times low in 2002. Then in 2003 I began visiting a nearer, swiss, renewed Casino, and I already hit the venue 30 times this year. With my net balance going as up as +3'500? till beginning of April, then vertically plummeting in the last month down to -4'500?. In that last same period I have begun playing BJ, but I still believe that's just a coincidence... as I actaully have not comparatively lost more with BJ than with the other games)

[humble]

If you think that -0.55% is about as bad as -2.70% then maybe card counting is not for you (yet). I mean, hey, +2.00% is about as good as -0.55% so why bother?

[Magician]

> In SUMMARY:
> I wanted to know whether the awareness that
> I want to optimize TWO consecutive hands
> combined together, and not just two
> individual unrelated ones, bears any
> "anticipated influence" on the 1st
> decision. (of course boiling down to nothing
> more complicated that indices, e.g. like hit
> 15 v 9 except if you also own a 12 after it,
> or if you're the last before a dealer's X
> and NoHoleCard...)

You can't have a better strategy for optimizing two hands "in parallel" than optimizing them "in serial" because you don't have any extra information. Now if you knew what the next card would be then you could devise a strategy for getting the best overall result from two hands.

Hope that helps.

[Magician]

> After all we have mostly French Roulette in
> Europe (i.e. single zero), and there the
> House Edge is around 2.70% IIRC, not much
> more bleeding than the 0.55% with the BJ
> rules I can find available (BS only, no CC).

That's ploppy thinking. It's over 5 times as "bleeding" and the effect compounds as you play through your stake over and over.

[Parker]

> After all we have mostly French Roulette in
> Europe (i.e. single zero), and there the
> House Edge is around 2.70% IIRC, not much
> more bleeding than the 0.55% with the BJ
> rules I can find available (BS only, no CC).

That's about like saying that there is not much difference between a stack of $20 bills and a similar sized stack of $100 bills!