8/17/2009 - Basic simulation project using combinatorial analysis - free download of version 2 of Excel spreadsheet (now open source)
4/3/2008 - 7 day trial of full version of Blackjack Game and Probability Computer is now available.
2/8/2008 - 15 day trial of full version of cdca (composition dependent combinatorial analyzer) is now available. (Free single deck demo of cdca is no longer available.)
5/1/2007 New - download composition dependent combinatorial analyzer (single deck demo discontinued) cdca information and download
The motivation behind the creation of this site is that I wanted a vehicle to run an interactive web program that I have created. I don't claim to be an expert in interactive web programs, html, web presentation, etc. I just simply wanted to see what minimal problems needed to be addressed to accomplish this. I have no idea where the site might go from here. I only hope that visitors find it informative and interesting in some kind of way.
How is blackjack different from other casino games? - Simply stated, each deck state produces a differing expected result. Some deck states are more favorable to the dealer, while some states are more favorable to the player. By contrast, in games such as craps and roulette the expected result is always a fixed amount and is always in favor of the house. Expected result means how much a bankroll is expected to change (plus or minus) as a percent of initial wager. A successful blackjack player will be able to identify when the deck states are favorable to dealer and player. He will bet more when the state is favorable to player and less when favorable to dealer. In games such as craps and roulette, there is never a favorable state to bet more on (assuming complete randomness.)
Basic strategy - Before a blackjack player can worry whether or not the expected result for a deck state is in his favor, he must know how to properly play his cards. Without acceptable playing of his hands, he would be in jeopardy of turning his favorable deck states to a negative expected result and an overall positive expectation to negative. Basic strategy is defined as playing your present card combination as well as you can given the knowledge of dealer's up card and the rules of the game. The program I have on this site gets the composition dependent basic strategy, which means it finds the strategy for whatever card combination is input. This is the best way to play given only the knowledge of your hand and dealer's up card. There is nothing wrong with playing this way, but there are so many possible card combinations it is too much to remember, so most players use a total dependent basic strategy, which is based on player's hard or soft total and dealer's up card. Total dependent strategy is slightly less efficient than composition dependent strategy but is far easier to remember. Generally, playing correct basic strategy does not eliminate to house advantage in blackjack, but minimizes it. In order to realize an advantage in blackjack, a player must count cards in order to identify deck states where he does have an advantage and bet enough on these to overcome the inital house edge. This is a bit of an oversimplified explanation, but the point is basic strategy is a key component of an overall successful strategy.
Blackjack Card Counting 101 - Blackjack is usually dealt from either 1, 2, 4, 6, or 8 full decks. Removing 1 or more twos, threes, fours, fives, sixes, or sevens from the starting deck state is generally favorable to the player. Removing 1 or more eights may be slightly favorable to player or dealer depending on number of decks, but to a very modest degree. Removing 1 or more nines is favorable to dealer to a modest degree. Removing 1 or more tens or face cards is favorable to the dealer as is the removal of 1 or more aces. Blackjack card counting systems make use of the above information to "tag" each rank with a value. The simplest systems use tags that could be valued at any combination of -1, 0, and +1. Such a system is known as a level 1 system. A more complicated system would use tags that could be valued at any combination of -2, -1, 0, +1, and +2. Such a system is known as a level 2 system. Similarly, it's possible to define a level 3 system and above. The best known and most widely used level 1 system is the Hi-Lo Count. It's tags are as follows: (2,3,4,5,6) -1, (7,8,9) 0, (T, A) +1. The initial count is computed:
Define initial running count as IRC IRC = (positive cards in initial deck) - (negative cards in initial deck) Specifically: 1 deck: 20 +cards (T,A), 20 -cards (2-6); Initial count = 20 - 20 = 0* 2 decks: 40 +cards (T,A), 40 -cards (2-6); Initial count = 40 - 40 = 0* 4 decks: 80 +cards (T,A), 80 -cards (2-6); Initial count = 80 - 80 = 0* 6 decks: 120 +cards (T,A), 120 -cards (2-6); Initial count = 120 - 120 = 0* 8 decks: 160 +cards (T,A), 160 -cards (2-6); Initial count = 160 - 160 = 0* *IRC of Hi-Lo for any number of decks is always 0The current count is kept as follows:
Define running count as RC Intially RC = IRC = 0 If a -card (2-6) is dealt, add 1 to RC If a (7-9) is dealt, RC is unchanged If a +card (T,A) is dealt, subtract 1 from RC Example (cards dealt one after the other): Initially RC = IRC = 0 2 is dealt, RC = +1 5 is dealt, RC = +2 7 is dealt, RC = +2 T is dealt, RC = +1 A is dealt, RC = 0 T is dealt, RC = -1 etc.For Hi-Lo, RC (running count) enumerates the imbalance between +cards and -cards regardless of how many cards remain to be dealt. A blackjack player may want to relate this imbalance, however, to the cards remaining to be dealt. For example if RC = +2 and there are 2 cards remaining to be dealt then the composition of the cards remaining is 100% +cards. If RC = +2 and there are 50 cards remaining to be dealt, then the composition of the cards remaining is about 40% +cards. In order to relate RC to cards remaining to be dealt, another parameter known as true count is used:
Define true count as TC TC = 52 times RC divided by (cards remaining to be dealt) [TC = 52 * RC / (cards remaining)] TC is not computed exactly because cards remaining is only an estimate. A blackjack player will need to devise a method he is comfortable with to compute a reasonable estimate of TC. TC (true count) is used to estimate the advantage or disadvantage the player has. Hi-Lo is called a 'balanced count'. To me a balanced count is one in which when the entire shoe is dealt and correctly counted, running count (RC=0). Hi-Lo fits this definition as long as initial running count (IRC=0). (Everybody and their mother defines Hi-Lo's IRC=0.) If a 'balanced count' ends up with RC=0 at the end of a shoe, then an 'unbalanced count' is one that ends up with RC not equal to 0 at shoe's end. An unbalanced counting system can be simpler than a balanced system because it may only consider running count without regard to true count (TC). An example of an unbalanced system is the KO Count. Typically, an unbalanced system defines its initial running count (IRC) such that at a given running count (RC) the expected value at that count first becomes favorable to the player. This RC is known as the 'key count' and is where a player would start to increase bets. An unbalanced count in general has varying degrees of accuracy at different points in the shoe, but there is a running count known as the 'pivot point' where it is as accurate as a balanced count. The accuracy exists only at the pivot, though. Computer simulation is used to blend the inherent inaccuracies into an overall system that works. Simulation has shown that unbalanced systems can work.The above is not meant cover card counting completely, but only to serve as a guide to what card counting is about.
Most knowledgeable blackjack players will agree that the value of a good betting strategy far outweighs the benefits of a good playing strategy, but I guess I've kept my interest in playing strategy because I wanted to see exactly where a blackjack player's advantages were for most common rules. I have developed a perfect play combinatorial analyzer that can compute overall expected values for any subset of cards as long as enough cards remain to complete any possible hands, using an optimal strategy for hit/stand/double and an optimal fixed strategy for splits. It can also compute individual hands for any subset. There is a trial download of this program available that computes and displays optimal composition dependent data. The initial motive in the creation of this site was to create an interactive web program capable of enumerating the correct composition dependent strategy for any player hand, common rules, and number of decks for a full shoe state. Basic full shoe composition dependent strategy for any player hand composition versus any dealer up card using common rules variations for any number of decks <= 41297762 can be accessed here. This program only outputs strategy, not any numerical data.
The optimal strategy for 8 or fewer decks when dealer's up card is 10 can be found here. I consider this method my intellectual property. The problem with composition dependent strategy is that it is basically inaccessible to the player because there is simply too much to remember. At least for dealer up card of 10, I have found a few steps a player can follow in order to replicate optimal basic strategy. Since the 10 is the most likely up card and 16 vs 10 is a close call, playing optimally has something to gain. The greatest gain will be for single deck and will be less for more decks.
Added 11-28-2005 Single deck insurance strategy using HiLo Count
Added 11-29-2005 Double deck insurance strategy using HiLo Count
Added 12-01-2005 4 deck insurance strategy using HiLo Count
Added 12-10-2005 Even money payout risk of ruin calculator for a fixed EV
Added 12-18-2005 6 deck insurance strategy using HiLo Count
Added 01-02-2006 8 deck insurance strategy using HiLo Count
Added 02-13-2006 KO Count Insurance Data
Single deck insurance strategy using KO Count
Double deck insurance strategy using KO Count
4 deck insurance strategy using KO Count
6 deck insurance strategy using KO Count
8 deck insurance strategy using KO Count
Added 11-06-2006 Article on number of possible shuffles in the game of blackjack
Comments and ideas: email kc@bjstrat.net
end for now