## cdca Help

cdca (Composition Dependent Combinatorial Analyzer) is a program that computes exact expected values for common rules variations in the game of blackjack. User inputs rules, shoe composition, and optionally player cards comprising a blackjack hand and clicks 'Compute' to display expected values. When the program loads it displays the computed expected values for a single deck using a default set of rules and no player cards. When no player cards are entered the program computes the overall expected values for all possible player hands. Any of these defaults can be changed and when the Compute button is clicked a new set of Player Expected Values / Dealer Probabilities is displayed depending upon user's input. The various possible user inputs are listed below.

## Settings and Rules

Decks - Number of decks (input directly) - Range is 1 to 41,297,762. The number of decks parameter furnishes a starting shoe composition. The only time number of decks has any bearing on what is computed is when 'Basic strat' (basic strategy) has been ticked, in which case expected values are calculated using the composition dependent (full shoe) basic strategy of the number of decks that has been input. When the program initially loads number of decks defaults to 1 and the strategy option defaults to 'Best strat' (best strategy.) Best strategy means that expected values will be computed given the actual shoe composition that has been input by the user. When user changes number of decks default is a full shoe for number of decks input. User needs to change shoe composition either by direct input or using the +/- buttons for one or more ranks in order to compute expected values for less than a full shoe. (The number of a rank present in the shoe cannot be set to a value larger than the maximum for the number of decks that has been input. The number of a rank present in the shoe cannot be set to a value less than 0.) Think of basic strategy as a fixed strategy that applies to any composition and is not necessarily best for that composition, whereas best strategy dynamically computes what is best (although splits use an optimized fixed strategy,) for any composition. All calculations are accurate as long as the input composition ensures that there is no possibility of running out of cards.

BJ Odds - Odds paid for a player blackjack.

S17 - If checked dealer stands on soft 17. If unchecked dealer hits soft 17.

ENHC - European no hole card. If not checked dealer peeks for blackjack. If dealer has blackjack then all non-player-blackjacks lose and the hand ends. If checked then dealer doesn't check for blackjack and the hand is played out. If it subsequently turns out dealer has blackjack then player loses all bets on present hand, including any additional bets made on splits and doubles.

EV - Conditioned on no dealer blackjack where applicable - If this checkbox is checked then program displays EV assuming dealer has checked for blackjack. This mainly applies to dealer up cards of ten or ace since those are the only 2 up cards where it is possible for a dealer blackjack. If the ENHC (no peek) option is selected or early surrender is allowed then unconditional EV will be displayed even if this checkbox is checked. Unconditional EV means simply that a non-player-blackjack loses to a dealer blackjack. In the case of ENHC or early surrender it makes no sense to say dealer has checked for blackjack before player's decision is made. Also overall EV is always the unconditional pre-deal expected value. For a player hand of 2 or more cards overall EV of the hand versus all up cards is displayed in the upper left corner of the 'Player Expected Values' section. When number of player cards input is 0 or 1 then EV displayed in the 'EV' row at the bottom versus each up card is always the unconditional expected value as is the value displayed in the upper left corner which is the overall expected value versus all up cards.

Compute mode - Selecting Best strat directs the program to compute using best possible strategy regardless of shoe composition. Selecting Basic strat directs the program to compute using full shoe composition dependent strategy regardless of shoe composition.

Depleted shoe split strat - Only applies if Basic strat is selected. Selecting Pre-split directs the program to compute basic strategy split hands using the same basic full shoe CD strategy as is used on non-pair hands. Selecting Optimal strat of 1st split hand directs the program to compute basic strategy splits using the best strategy of the 1st hand of a split in a full shoe.

Auto winner

• None - If selected no player hand wins automatically.
• 5 card - If selected any 5 card player hand wins automatically, including split hands
• 6 card - If selected any 6 card player hand wins automatically, including split hands

Doubling

• DO2 - If selected doubling is restricted to 2 cards
• DAN - If selected doubling is permitted on any number of cards

• Restrictions for hand total
• None - Double on any total
• Hard 9-11 - Doubling restricted to hard hards totaling 9 to 11
• Hard 10-11 - Doubling restricted to hard hards totaling 10 or 11
• H 9-11 + Soft - Doubling restricted to hard hards totaling 9 to 11 or any soft hand
• H 10-11 + Soft - Doubling restricted to hard hards totaling 10 or 11 or any soft hand
• Hard only - Doubling restricted to hard hards only

Splitting

• Allowed splits aces - Number of allowed splits for a pair of aces
• Allowed splits 2-10 - Number of allowed splits for a pair of ranks 2 through 10

• After splitting
• DAS - If checked doubling after splitting is allowed. If unchecked no doubling after splitting is allowed.
• HSA - If checked hitting split aces is allowed. If unchecked a split ace is dealt one and only one card.
• Double after splitting aces - If checked doubling after splitting aces is allowed. If unchecked doubling after splitting aces is not allowed. Both DAS and HSA must be checked for doubling after splitting aces to be an option.

Surrender

• Allowed vs 2-9 - If checked surrender is allowed versus dealer up cards of 2-9. If unchecked surrender is not allowed versus 2-9.
• Versus 10
• No surr - If selected no surrender is allowed versus up card of 10
• Late surr - If selected late surrender is allowed versus up card of 10
• Early surr - If selected early surrender is allowed versus up card of 10
• Versus Ace
• No surr - If selected no surrender is allowed versus up card of Ace
• Late surr - If selected late surrender is allowed versus up card of Ace
• Early surr - If selected early surrender is allowed versus up card of Ace

## Shoe Composition

Shoe composition may be changed one card at a time by clicking the -/+ buttons beneath each rank textbox. Clicking '-' removes a card and clicking '+' adds a card. Number of each rank present in the shoe can also be set by directly editing any rank textbox. The limits of what can be input depends upon the number of decks that is entered.

Full shoe - Clicking this button resets shoe to full.

## Player Cards

Click any of the 10 rank buttons to deal a card to player. Total of player cards is displayed in textbox to the right of player cards textbox. Player cards are not immediately removed from the shoe composition but they are automatically removed when the 'Compute' button is clicked. If the user has entered cards in the player hand and set shoe composition such that it's not possible to deal player's hand from the shoe, then a message is displayed that 'hand cannot be dealt' and no calculation occurs. In that case user needs to change shoe composition and/or player hand composition to values where it's possible to deal all of the cards in the player's hand from the displayed shoe composition.

• Undeal - Removes the last card dealt to player
• Reset - Removes all player cards and sets player hand to empty

## Compute button

When the 'Compute' button is clicked a new set of Player Expected Values and Dealer Probabilities is computed and displayed depending upon what the user has input. If number of player cards input is zero or one when 'Compute' is clicked then program computes player's overall EV. If two or more player cards are input then the expected values for that particular player hand are computed and displayed. Any cards in player's hand are automatically removed from the displayed shoe composition after the 'Compute' button is clicked but before computation begins. The reason player cards are not removed before the 'Compute' button is clicked is because it is felt that it makes for a cleaner overall user interface. All probabilities are dependent upon shoe composition and rules.

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