Quote:Dieter"optimal" strategy either requires next-card knowledge (extremely rare - marked cards or end decking), or card counting & index play (somewhat less rare, but still challenging).

This too is a solved problem. Almost every card counting technique suggests certain index plays - deviations from basic strategy, based on seen cards.

The first on the list is almost always insurance - there are times when it is statistically optimal to take it, and there are other times when it is not.

It makes sense. So the so-called optimal means to increase the chance of guessing next card so to increase the expectation for pay for each hand? And why I did wrong is to assume knowing the next card for 100%, that's will definitely cause over 100% payout. Thanks.

I haven't read all the thread but in theory you need to evaluate the best course of action for all permutations of your cards and the dealer's up-card. If you were working it out for perfect strategy it's an iterative process. For instance only after you've decided what to do with (say) 5 7 9, 5 7 8, 5 7 7...5 7 A, could you go back to 5 7 and see what you should do.Quote:ThatDonGuy...record the highest pay...for 10,000,000 times...

I guess your method is to record at each stage the outcome for the various runs of cards for all combinations the player might have given the start deck (and say shuffle up after each hand). The problem is 10 million hands is never enough - for instance you would only get A-A vs A about 4500 times.

Blackjack is fairly volatile, at the moment I'm trying to work out, using basic UK strategy, what the House Edge assuming you shuffle after every hand. Each run is 1 billion hands/shoes and I'm getting a range of results, one can work out the average number of winning Blackjacks should be 4 532 299.

Expected # hands Money Won Money Lost Tie BlackJack (win)

Average

.461 501 900% 1 000 000 000 451 724 075 524 322 445 88 112 610 4 532 223

Each Run

.004 585 839 1 000 000 000 451 744 980 524 309 673 88 115 784 4 531 923

.004 623 015 1 000 000 000 451 721 225 524 324 873 88 110 953 4 532 042

.004 619 640 1 000 000 000 451 726 848 524 325 949 88 105 458 4 531 964

.004 596 668 1 000 000 000 451 721 881 524 318 569 88 104 321 4 533 334

.004 633 158 1 000 000 000 451 704 160 524 323 531 88 121 691 4 532 414

.004 592 613 1 000 000 000 451 734 302 524 311 161 88 109 542 4 532 283

.004 654 202 1 000 000 000 451 715 131 524 343 361 88 120 520 4 531 601

Quote:konglifyThe reason why I start this code is I want to find the optimal strategy instead of the basic one. So what is the main difference between optimal and basic strategy?

That depends on your definition of optimal strategy. If it is "determine what to do with the next card based on your hand, the dealer's up card, and the cards remaining in the deck," then not only would you need to know exactly how many of each card is left in the deck at every point, but you would need to be able to calculate the probabilities instantly at that point. Nobody is smart enough to do that in their head (and even if somebody could, he would be asked to leave for card counting), and you can't use any sort of device to calculate it for you when you are at a table.

Note that basic strategy and optimal strategy are the same thing when the deck is full - but that assumes you are the only player at that table, as any other players' cards would have to be taken into account.

Quote:konglifyIt makes sense. So the so-called optimal means to increase the chance of guessing next card so to increase the expectation for pay for each hand? And why I did wrong is to assume knowing the next card for 100%, that's will definitely cause over 100% payout. Thanks.

It goes back to one of the unique traits of blackjack - the cards are not shuffled after every hand.

As cards are dealt, they are removed from the undealt deck - based on what has been played, we can infer the composition of the undealt deck, and as that composition shifts, we can make adjustments both in what plays to make in a situation (index plays) and how much is wagered (to minimize the house win and maximize the player win).

If you don't know how the undealt deck differs from the full deck, use basic strategy.

If you do know how the undealt deck differs from the full deck, an index play might be in order.

One thing though, the rule set does determine the win%. For example adding Late Surrender actually reduces the win%, but causes the House advantage to reduce. This because Surrendering is a better play in some cases.