This project is inspired by tabletop role-playing game "Soleil Noir". See https://soleilnoir-jdr.blogspot.com/
This project attempts to model some actions performed in this game. In particular, it allows producing statistics on these actions.
For now, this project only model card draw, which allows knowing probability of success of a card draw.
This program executes multiple random card draws. Each card draw consist of:
- a number of cards to draw from a classical 54-cards deck
- a difficulty for the draw (see combination/difficulty below)
- a combination strategy, which define how we compute the force of the hand of card that has been drawn
By comparing the force of the hand against the difficulty to pass, we can define if the draw was a success or not. By performing multiple draw, we can compute a success rate for each experience. This gives us an estimation of the probability of success of card draw given a difficulty to pass, and a number of cards to draw.
Soleil Noir system uses a classical deck of 54 cards, consisting of 52 "normal" cards, and 2 jokers. Normal cards have a value (in ascending order of their force: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace) and a symbol (club, spade, heart, diamond). When representing a card value in this program, we usually use a single character in this order: "2", "3", "4", "5", "6", "7", "8", "9", "0", "J", "Q", "K", "A" (value 10 is represented with a "0" to prevent confusion with the Ace card).
In Soleil Noir system, a set of cards can form together a combination, defining how strong this set of card is. A combination of card consists of several cards with the same value. The more cards in the combination, the better. In case of a tie between combinations, the combination using the stronger value is the better combination. Therefore, a pair of Aces is better than a pair of 2, but a pair of 2 is better than a single Ace.
When defining a difficulty for a draw, we just define the minimum combination to get. If drawn cards are enough to produce a combination at least as strong as the difficulty, then the draw is a success.
In this program, when representing a combination, we usually use this pattern: number_of_card[card_value_symbol]. For instance, 2[A] represents a pair of aces.
Combination strategy represent how we pick the combination of a hand based on the set of cards in this hand. Default rule in Soleil Noir is to pick the best combination existing in current hand without further modification. But sometimes other rules may apply (when character has some advantage or disadvantage for instance), modifying how cards are considered. When running this program, we must define which strategy is applied.
The implemented strategy are:
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"default" strategy:
This is the most common strategy, applied when not special rule is involved. With such strategy, we simply look at the cards in hand, and count which card value is present with the higher quantity. In case of a tie, we pick the value with higher force. For instance, with a hand of "Queen of club", "Queen of heart", "10 of spade", "10 of diamond" and "Ace of club", the final combination is 2[Q] (there is 2 possible combinations with 2 cards: a pair of Queen, or a pair of 10 (Ace has only one card) ; since the Queen is stronger than 10, the final combination is the pair of Queen). When Joker is present in hand, it can take any value, meaning it can enhance existing combination (for instance in previous example, if the hand also possessed a Joker card, the final combination would be a 3[Q], because Joker would be converted into a Queen card).
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"disadvantage" strategy:
This strategy is the implementation of some disadvantages which exist in Soleil Noir. With such strategy, one of the four card symbols is treated as a disadvantage symbol. When performing a card draw, and before defining the combination of the hand, we must throw away from the hand any card with this symbol (excepted Aces). Otherwise, we apply the same rules as in "default" strategy. For instance, with a disadvantage on symbol "club", and a hand of "Ace of club", "Ace of heart", "King of club", "King of heart", "King of diamond", the final combination is 2[A] (the King of club is removed because it is a club card, but the Ace of club is not removed because it is an Ace).
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"advantage" strategy:
This strategy is the implementation of some advantages which exist in Soleil Noir. With such strategy, one of the four card symbols is treated as an advantage symbol. When performing a card draw, and before defining the combination of the hand, we must convert some cards into a new value: all cards with the advantage symbol (including Joker if it is converted into a card with this symbol) are converted into card with the same symbol, but with the value of the higher card in hand with this symbol (including Joker if it is converted into a card with this symbol). For instance, with an advantage on symbol "club", and a hand of "King of heart", "Jack of club", "2 of club" and "Joker", the final combination is 4[K] (the Joker is converted into a "King of club", then all club cards are converted into the club card with the higher value, ie the King of club... the hand is therefore now a hand with one "King of heart" and three "King of club").
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"advantage-limited-joker-before" strategy:
(/!\ Caution: this is a personal interpretation of Soleil Noir rules, and not the official rule. I have implemented this custom rule interpretation because I feel the original "advantage" strategy is too powerful, and too complex to resolve during card draw. /!\)
This strategy is the implementation of some advantages which exist in Soleil Noir, with a personal variation. With this strategy, we apply the same rule as in "advantage" strategy, where cards with the advantage symbol are converted into the best card with this symbol. However, with this specific strategy, we no longer consider those converted cards as compatible with normal cards. If player choose to apply his advantage, he must create a combination with only cards with the advantage symbol. For instance, with an advantage on symbol "club", and a hand of "King of heart", "Jack of club", "2 of club" and "Joker", the final combination is 3[A] (if the player had chosen not to apply his advantage, the best combination would be a pair of King by converting Joker into a King - however, when applying advantage, player can create a combination made of clubs, which would be a "Three-of-a-kind of club" because 3 club cards are present in the hand (2 club cards and 1 Joker which can be converted into a club card - it is no longer interesting to convert the Joker into a "King of club" because the King of heart cannot be applied in the combination of advantage cards (we cannot put this heart card into the "Three-of-a-kind of club")) - furthermore, if the player choose the Joker to be an "Ace of club", all other club cards are converted into an Ace, producing a combination of "Three-of-a-kind of club" evaluated as a "Three-of-a-kind of aces").
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"advantage-limited-joker-after" strategy:
(/!\ Caution: this is a personal interpretation of Soleil Noir rules, and not the official rule. I have implemented this custom rule interpretation because I feel the original "advantage" strategy is too powerful, and too complex to resolve during card draw. Furthermore, this is the strategy I personally use when being a Game Master in Soleil Noir. /!\)
This strategy is the same as "advantage-limited-joker-before" with a small variation: Joker value is defined after cards with the advantage symbol have changed their value. This means we can no longer converts all advantage cards into an Ace combination only by defining the Joker as an Ace of the advantage symbol. Here the Joker should instead take the value of the higher card of the combination. For instance, with an advantage on symbol "club" and a hand of "King of heart", "Jack of club", "2 of club" and "Joker", the final combination is 3[J] (the two club cards are converted into a "pair of club", evaluated as a "pair of Jack" - then the Joker is added as another club card, converting this hand into a "three-of-a-kind of club", evaluated as a "three-of-a-kind of Jack").
To run this program with different configuration, you should edit configuration file: src/main/resources/stat-config.properties
Configuration are:
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nb-try: (integer) Number of repetition of each experience to perform statistics. For instance, if this value is 100, this means that we will perform 100 draws for first difficulty with first number of cards, 100 other draws for second difficulty and first number of cards, etc... With a higher amount, the result will be more precise, but the program will take longer to finish (please check binomial distribution variance for an estimation of the precision).
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nb-card-min / nb-card-max: (integer/integer) Those numbers define the range of card numbers used for those statistics. For instance, with values 1 and 12 (respectively), program will perform statistics when drawing only 1 card, when drawing 2 cards, ... and when drawing 12 cards.
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difficulties: (list) This list define all difficulties against which statistics will be performed. For instance, "1[A],2[2],2[A]" means statistics will be performed against difficulties "one-card of Ace", "pair of 2" and "pair of Aces".
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combination-strategy: (string) Define which combination strategy is applied during those statistics. See section "Strategy" for list of strategy names and signification.
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nb-decimal-digit: (integer) Define how many decimal digits (after comma) are printed in export result. For instance: 100% for 0 digit, 100,0% for 1 digit, 100,00% for 2 digits, etc... Caution: this parameter is only used to define how results are printed, and does not indicate anything about result precision (result precision depends on parameter nb-try).
When program is completed, a result csv file will be generated in directory "export".
File name has this pattern: "soleil-noir-statistics_<strategy_name>_<nb_try>.csv", where <strategy_name> and <nb_try> are values of those parameters, provided when the program was run.
The result file is a csv table defining success rate (in percentage) for each number of drawn cards against each difficulty.
I run this program for each strategy and with a sample size of 10 000 000 draws. Those results are provided in export folder. With such sample size, we can expect a margin of error of 0.04% (with a confidence level of 99%) / a margin of error of 0.1% (with a confidence level of 99.999999%). Since results are provided with a precision of 1%, we can suppose all digits from those results to be significant. (For instance, we should theoretically find a success rate of 33.333...% when drawing 1 card against 1[J] difficulty. With a sample size of 10 000 000 draws, we should almost always find a result of "33%". With a smaller sample size like 1 000 draws, we often find a result of "32%" or "34%").
(See https://en.wikipedia.org/wiki/Margin_of_error for calculation of margin of error)