What mathematics is involved in techniques like Illustrious 18 and effect of composition-dependent stratagies

[Killman2002]

The Illustrious 18 and composition-dependent strategies are based on the mathematical principles of card counting and basic strategy.
The Illustrious 18 is a list of eighteen basic strategy deviations that were developed by the mathematician Don Schlesinger. These deviations are based on the count and are designed to increase the player's advantage in specific situations.
Composition-dependent strategies involve taking into account the specific composition of the player's hand when making decisions. For example, if the player has a 16 that is made up of two 8s, they may choose to split the 8s instead of hitting or standing.

 

[CR7]

Indeed, the Illustrious 18 and composition-dependent strategies are deep-rooted in the mathematical principles of card counting and basic strategy in blackjack.

When it comes to card counting, the main idea is to track the relative numbers of high and low cards that remain in the shoe. This can give the player an advantage if there are more high cards left, as high cards generally benefit the player (e.g., the likelihood of getting a natural blackjack increases with more tens and aces in the shoe). Basic strategy is the statistically optimal way to play based on your hand and the dealer's upcard, regardless of the true count.

The Illustrious 18, created by Don Schlesinger, is a set of deviations from basic strategy that are meant to be used in specific high-count situations to maximize the player's advantage. These deviations aim to take advantage of the increased probability of certain advantageous outcomes, such as doubling down on a hard 12 when the count is high because the deck is rich in tens and aces.

Composition-dependent strategies, on the other hand, consider not only the value of your hand but also the specific cards that comprise it. For example, a pair of 8s in blackjack is typically a tricky hand. If you apply a composition-dependent strategy and the count is high, you may split the 8s to increase your chances of getting 18 with each hand.

These strategies involve a balance of understanding basic strategy, card counting, and adjusting your play based on the specific composition of your hand in correlation with the count. By incorporating these strategies effectively, players can further enhance their edge over the house in favorable situations.

 

[swift]

I think Illustrious 18 involves identifying 18 specific situations in blackjack where the odds are most in favor of the player, based on the dealer's up card and the player's hand. This technique uses basic probability to calculate the likelihood of the player winning or losing in each situation.