Vira is a Swedish card game of the trick-taking type E.g. similar to Contract Bridge or Spades. It is a 3 player game with each player dealt 13 cards and the remaining undealt stock of 13 cards to be used by the players to improve their hands. A descendant of the card game Boston, it has a large number of bids that can be made. Depending on the variant (Stockholm, Gothenburg, Iceberg) there can be 40 to 47 bids.
I am posting a simplified bid table for the game created by Raymond Gallardo, as it encapsulates the bids for the question well. The Pagat & BGG websites have details on the game play and more details on the rules.
Vira Bidding Table:
While the bids seems numerous and complicated they can broadly be grouped by the type of bid and the number of tricks as the following -
(1) Buying (Begär) Bids - In which the player can buy i.e. discard a number of cards face down and take the same number of cards from the undealt stock.
(1.b.) Gambling Bids (Tourné, Double & Triple) - A card (or 2 or 3 for Double or Triple) is turned up and the player chooses the suit displayed or one of the suits as the trump suit. The player must starting with the turned up cards can buy more cards from the stock to improve their hand.
(2) Take the stock (Gask, likely from the Spanish term Casco from the game Hombre) - Retains a number of cards (0-6) picks up the remaining stock of 13 cards and then discards down to 13 cards.
(3) Solo - The player making the bid will play with just the 13 cards in their hand and make no exchanges to improve.
Vira Bids Summary Table:
And for each group of bids the player can choose to make -
(1) Positive bids - play to win 6 to 13 out of the total 13 tricks or
(2) Negative bids - play to lose all 13 or 12 out of the 13 tricks to be played.
As per most descriptions the bids in the bid tables are arranged based on statistics collected during gameplay.
While I can intuitively understand the higher ranking of bids that need to win a higher number of tricks. As this requires a hand to have a larger number of higher ranked cards E.g. - A, K, Q, J which is statistically rarer.
Within the bid types - I can also understand the increased rank of the Solo bids as without the opportunity to exchange lower ranked cards from the stock, it becomes statistically more difficult to make the bid.
However I am not clear of the statistical/mathematical soundness of the ranking between the Buying (Begär) bids & Take the stock (Gask) bids.
As per the bid table the Take the stock (Gask) bids are of a higher difficulty level than the Buying (Begär) bids. Intuitively, this doesn't make sense to me as I believe taking the entire stock gives you more optionality to find higher ranked cards than 'buying' cards when you discard a card and are picking up cards sight unseen, in which case your bid is less likely to be successful.
Stated simply - How can I model the increased (or reduced) probabilities of getting a hand by (a) picking up more cards vs. (b) discarding a card and then picking up a card.
I've tried to model this with a simpler version of the game with just 16 cards (A, K, Q, J) instead of the whole deck of 52, but I'm stuck in modeling a pure discard vs. a pick up and discard.