Basic Strategy Algorithms

Hi,

I am interested in the methods/algorithms used to calculate basic strategy. My reading so far has been limited to thorp, griffin and wong.

From my initial research it seems that basic strategy is calculated using combination analysis.

For example I get dealt 10 & 3 and the dealer has a 5 showing:

1. Standing is purely based on the probability of the dealer beating the player (in this case the dealer has to bust) which can be calculated from all of the possible permutations of the 48/49 (us/euro) cards remaining in the pack and their probability of occurrance.
2. Hitting we have to work out all of the permutations of cards available to the player and their probability of occurrance. Additionally we have to compare the probability of the dealer beating the player for each combination. From this we can obtain an overall expection for hitting.
3. Doubling can be calcuated the same way as hitting except that we double the stake and only allow the player to take one card.
4. Pair splitting is calculated by recursivley determining the expected return for every combination of decisions available to the player and their probability of occurance using the methods described in 1, 2 and 3.

The optimum result of 1,2,3 and 4 is then incorporated into basic strategy.

The only variation on this approach which I can find is dependant on whether we use a basic or zero memory strategy. The former taking into account how cards dealt during the course of a hand can affect our expectation.

The affect of a card count on basic strategy can then be calculated by recalculating basic strategy from a depleted deck e.g. we may remove an ace or a 10.

I have two questions:

i. Is this the only way people have managed to calculated basic strategy successfully or are there other algorithms / methods?
ii. Can anyone suggest good books / documentation / articles about methods used to calcuated basic strategy? (I have read most of the stuff on bjmath.com)

Any help would be most appreciated.

Thanks

Mark

You've read the right people (except for Braun, who virtually started it all -- but his stuff is out of print) and have the right understanding.

The pair-splitting is extremely complicated,of course. Today, we also have BS by simulation, but combinatorial analysis, when done properly, remains the most precise of the methodologies.

And, we have several sources of "perfect" BS.

Don

Thanks for your response.

I was just wondering about the simulation algorithms - because to my way of thinking this may be a better way to calculate basic strategy and the variations with count. To give an example - I might assign a value of +1 to a two and also the same value to a 6. However even though I count them as the same I am going to use up more twos than sixes playing basic strategy.

This may or may not have an affect on basic strategy and expectation however combination analysis is not going to tell me what impact this will have and its magnitude.

So I was wondering if anyone has actually written an successful algorithm to calculate basic strategy by simulation and if so what their methodolgy was.

Thanks

Mark

By definition BS refers to the optimal play given knowledge, off the top of the pack, of nothing but your two-card holding and the dealer's upcard.

To determine BS correctly by simulation, therefore, requires reshuffling of the pack (regardless of how mnay decks used) after the completion of every hand.

Don

However even though I count them as the same I am going to use up more twos than sixes playing basic strategy.

I don't believe this is true. Not if the cards are randomly shuffled. (It's possible to have many more twos in a hand than sixes, but that doesn't mean more will, in fact, be used on average.) In fact, the reverse may be true, because the dealer's last card is more likely to be a six (which can bust) than a two. But a) this is a tiny, tiny effect, and b) careful analysis proves this will have absolutely no effect on basic strategy.

The most likely last card for the dealer is a T, so the average count goes down very slightly on each round. This was dubbed "The Leib effect" in an issue of BJF -- also guaranteed to have zero effect on basic. It can have a slight effect on how we interpret a count of zero, though.

For this reason, it's possible to generate basic without shuffling after every round (which can be very time consuming), but you need to use a fixed number of rounds per shoe, instead of a cut card, and you need to set the number of rounds low enough to guarantee the shoe will never run out of cards.

So I was wondering if anyone has actually written an successful algorithm to calculate basic strategy by simulation and if so what their methodolgy was.

I don't have either program, but I understand SBA and Blackjack 6-7-8 do this. And the results are the same as CA, once you get over little nits about comp dependant vs. total dependant strategy, and the cut card effect.

ETF

Are card counting techniques based on the same "reshuffle after one hand" scenario? If not, how do they differ from Basic Stratigy analysis?

whatsoever of what you are asking. None.

Don

(okay I got it right this time :)

Mark,

Rather than doing permutations with each possible card, one can get a big savings by considering the similarities in the ranks, and using recursion. Here's what I have done, using your example, in some very rough pseudocode:

EvaluateHand(PlayerHand, UpCard, Deck)
{
if (PlayerHand is done drawing) then

return (EV of hand against upcard, drawing from Deck)
else

EV = 0;

loop NextCard from Ace to ten:

EV = EV + EvaluateHand(PlayerHand + NextCard, UpCard, Deck - NextCard) * Probability of drawing NextCard

end loop

return EV
end if
}

For pair splitting involving resplitting, I do the following:
(Assume that Deck already has the two cards of rank PairRank drawn out of it)

EvaluatePairSplit(PairRank, Deck)
{
Initialize EV = 0.0
ProbOf2Hands = P of drawing 2 consecutive cards NOT of rank PairRank
ProbOf3Hands = 2 * P of drawing PairRank * P of drawing NonPairRank^2
ProbOf4Hands = 1.0 - (ProbOf2Hands + ProbOf3Hands)
Create a new player hand, consisting of 1 card of rank PairRank

Loop NextCard from Ace to Ten:

initialize NextCardEV = 0.0

If (NextCard = PairRank) then

ProbOfEvent = 0.0

else

ProbOfEvent = (Probability of drawing NextCard / [1.0 - Probability of drawing PairRank])

end if

CopyOfPlayerHand = PlayerHand + NextCard

CopyOfDeck = Deck

NextCardEV = NextCardEV + (EvaluateHand(CopyOfPlayerHand, UpCard, CopyOfDeck)) * 2 * ProbOf2Hands

CopyOfDeck = Deck - PairRank

NextCardEV = NextCardEV + (EvaluateHand((CopyOfPlayerHand, UpCard, CopyOfDeck)) * 3 * ProbOf3Hands CopyOfDeck = Deck - PairRank

CopyOfDeck = Deck - (2 cards of PairRank)

NextCardEV = NextCardEV + (EvaluateHand((CopyOfPlayerHand, UpCard, CopyOfDeck)) * 4 * ProbOf4Hands

EV = EV + NextCardEV
end loop
}

This should give you the general idea. Remember of course you need ways to tell the EvaluateHand routine whether it can or cannot double after splitting, etc.

Hope that helps. I have BJ simulator on the brain these days so I was in the sharing mood.

M.

Do simulation programs which predict card counting outcome also reshuffel the cards after the first hand dealt?
I was giving you the opportunity to further explain the nature of simulated play.

The main reason I asked the question is that wongs professional blackjack book contains basic strategy combined with information about when to vary strategy with the count(Griffins book also contains tables of the affect of removing cards particular from a full deck). (Im not sure whether this can be called basic stategy as it includes a count - maybe im just getting my terminology mixed up). I havent got any of wongs software however I assume he used combination analysis - and if this is the case he must make some kind of assumption about what cards are removed from the deck for a particular count unless he calculates the probability of say 4 twos remaining in a pack at a count of 2.

Am I right in assuming this or is there a more rigorous way of determining strategy variations with count or am I in barking up the wrong tree?

Thanks

Mark

Generally, a simulator will play through some large number of shoes while flat betting. At the start of each hand, it will determine the count at that hand. When the hand finishes, win or lose, the result is recorded in a variable for that count.

At the end of it all, we examine each one to determine the advantage. For instance, if between a true count of +3.00 and +3.99, the player has a 1% advantage, we then make a note in our betting system on what to bet if the true count (after dropping the decimal place) is +3.

With our betting system in place, we then run a simulation with the bets as appropriate to determine an overall advantage.

As far as calculating effects of removal of certain cards (which lead to the counting values), we don't "shuffle" per se - rather, we take a deck, remove a single card of whatever rank we are looking for, then we multiply the probability of getting each possible hand against each possible upcard by how much that hand is worth, and adding it all up. So as the program explores each possible "branch", in a sense, it starts at the beginning - with a freshly shuffled deck with one of those cards removed.

A similar tactic is used for simulating a specific hand, except we remove all the relevant cards from the deck at the start - that is, if we are testing the value of T + 4 vs 9, we remove a ten, a four, and a nine from a blank deck, then figure out every possibility from there.

M.

these are what we'd call "deviations" from basic strategy.

To calculate each deviation, I imagine it is done by simulation.

M.

...by some of Walter's claims. If he argues with the best simple explanation of why betting systems and progressions fail (unless tied to deck composition somehow), he should go to bjrnet.com and get on the voodoo board or perhaps visit psiops.com, or psitech.com, and learn about technical remote viewing and magick (which don't apply too well in casino conditions---ask Dr. Lee S. Briliant M.D. former consultant with the SRI remote viewing team and former member of one of Uston's count teams).

.. or what he believes in. If he asks me a question about how computer simulations work, I will give him an honest answer.

I am an athiest, but I ask questions about Bible interpretation all the time. I expect honest answers from those I ask, and I get them. Whether Walter believes (or professes) to believe in card counting strategies is irrelevant. If he asks a question about things I believe in, I will give him an answer.

M.

... you should get a copy of Professional Blackjack, by Wong, which contins a meticulous explanation of how he determined his indices (as well as answers to many other related questions). SBA will also generate indices, generally considered slightly more accurate nowadays. You could find the site for Statictical Blackjack Analyser and d/l a trial version, I believe. You might find an explanation in the help files.

ETF

How are changes in Basic Strategy (based on the count) determined?
(Note: I assume others besides myself will benefit from your responses in this thread.)

Instead of doing ANY research, purchase several more good books, including one or more that teach how to play, practice, count, etc.

About remote viewing. I have the intro. video. Can it be used for blackjack?