• How To Play Blackjack Strategy
• Long-term Roulette Strategy
• Blackjack Strategy Card
• Basic Blackjack Strategy Chart

Blackjack strategy Basic strategy. Each blackjack game has a basic strategy, which prescribes the optimal method of playing any hand against any dealer up-card so that the long-term house advantage (the expected loss of the player) is minimized. Blackjack Strategy: Hard Hand Double Down If you have a total of 10, you will want to double down unless the dealer has the same 10 or an Ace as their upcard. In this case, take hits and play by the above-mentioned rules depending on your total. If you have a 10 against a dealer’s 9 or less, you should double down, if allowed.

• Long-term BJ strategy. House advantage kicking in in the long term, except 70 hands is a joke in the long term. Thing in party poker blackjack many years ago.
• The problem here, from a mathematical perspective — aka my favorite perspective — is that blackjack strategy is constructed to give you an edge if you adhere to it without deviation and play for a long, long time. It’s like a thousand monkeys on a thousand typewriters — eventually they’re going to write A Tale of Two Cities.

Card counting is meant to achieve two objectives – to help the player assess when to raise his/her bet based on the count and to help him/her assess when to use certain variations to the basic strategy, again taking into consideration the count. To employ variations to the basic strategy at the proper moment of time will usually benefit the player.

Let us illustrate with an example. Imagine that you participate in a six-deck game with S17 and you hold 7-4, while the upcard of the dealer is an Ace. In case you conform to the basic strategy rules, you need to abstain from action in these conditions. At the same time, at your table there could be someone who decides to double down on that hand and has a success. Logically, you would blame yourself for not being decisive and courageous enough to double down on the same hand – you would have doubled your balance. However, professional blackjack players claim that your long-term win from hitting 7-4 represents 0.147 times the original bet you placed, while the long-term win from doubling down on the same hand represents 0.127 times that bet. Or, in case your original bet is $100, your average gain for that hand will be $14.7, while if you double down, you will gain $12.7 on average (13.61% less than what you would have scored as profit, in case you followed basic strategy guidelines).

If you happen to hold such a hand, you may double down, when your true count is +1 or higher! If you play this hand in such a manner, your expectation will move up to 0.148 from 0.147. Although the change may seem insignificant, you may play the hand in such a way by placing a larger bet. This is just one among the 18 basic strategy variations, which experts recommend. In case you play a six-deck game, all 18 variations could ensure you over 33% to the profit, which basic strategy alone grants you. These variations, which could add even more in a single-deck or a double-deck game, are famous for being the Illustrious 18. We shall dig deeper into them right after we discuss four variations to the basic strategy for games having the option to surrender. These four variations are known as the Fab Four.

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The Fab Four

While the Illustrious 18 are variations to the basic strategy for any blackjack game, the Fab Four are variations to help a player increase his/her profit in a game where the surrender option is offered. Don Schlesinger came up with the ”Fab Four” term, which refers to the top-four late-surrender plays based on the Hi-Lo system. You may play in such a manner, in case your true count is 0 or higher. Let us have a look at the Fab Four variations to the basic strategy, which are used in multi-deck games:

1. You need to surrender, if your hand is 15, the dealer's upcard is 9 and your true count is +3.

2. You need to surrender, if your hand is 15, the dealer's upcard is 10 and your true count is 0.

3. You need to surrender, if your hand is 15, the dealer's upcard is an Ace and your true count is +2 (in S17) or -1 (in H17).

4. You need to surrender, if your hand is 14, the dealer's upcard is 10 and your true count is +4.

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The software used to generate the charts, as shown under strategy can be downloaded here. This software can be used to prove that by playing Blackjack, it is possible to beat the dealer on the long term under certain conditions. As far as I know, Blackjack is the only game offered by casinos, where this has been mathematically proven. This software was written in C in 1992 during my studies of physics for a seminar about probability calculations.

Download the sources from here (20.4 KB). The following executables can be build:

• bbjd: tool to calculate probabilities and expectations interactively.
• basicbbjd: the same as bbjd but for the basic strategy.
• simbj: simulation of a Blackjack player using the best strategy.
• basicsimbj: the same as simbj but for the basic strategy.

These executables have a very simple UNIX-like command line user interface.

Disclaimer

This software may be used to understand and to learn the strategies of how to beat the dealer. The sources are published under the GNU Public License which means that this program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
This software should work on every computer younger than myself. The only tools you require are a C compiler. The probability calculator has no dependencies, not even to the standard C library. Minor modifications to the Makefile may be necessary. If you are able to compile a simple Hello World program, you are able to compile this software on your computer. I will not answer any questions about how to build it on your architecture.

Bugs

This program has been released to public in 1998. Since then it has been downloaded a few times daily. Nobody ever reported a bug, except for the unser interface. I therefore assume that the mathematical engine of the program is bug free.

How To Play Blackjack Strategy

Guarantee

I will pay 100 US Dollars to the first person showing a bug in the mathematical engine of this software, namely probability.c.

Accepted bugs are:

1. Crashes or bogous results using correct input as defined in probability.h.
2. When the decision maker of this software instructs the player to do wrong decisions, such as buying, staying, doubling or splitting.
3. If an alternative solution makes better mathematical decisions than this software^*.

Long-term Roulette Strategy

This guarantee does not apply on:

Blackjack Strategy Card

1. Wrong results caused by rounding errors on your hardware.
2. Bugs in the user interface.
3. When other Blackjack rules, than described here are beeing applied.

This offer is voluntary and no legal claims can be derived from this guarantee, therefore no law is applicable. I will publish the name of this person and/or add a link to a page of his choice.

Basic Blackjack Strategy Chart

^* one must provide a solution using an API compatible to simulate.h. The alternative solution must show a considerabely higher total gain than this Blackjack simulator after at least 10 million simulated games with exactely the same content in the shoe.