Open-pile probability.
The probability of the next card improving your hand depends on three observable variables: the cards visible so far, the open-pile card you are considering, and the closed-deck size. This piece walks through all three.
The three variables
Three observable variables drive every pick-from-pile decision:
Visible cards
All cards dealt plus all cards discarded. The deck above the current open-pile card is part of the visible set. The desk assumes a four-handed game with one open pile and one closed pile.
Open-pile card
The single card you would pick up. Its identity matters at three levels: rank, suit, and proximity to the cards already in your hand.
Closed-deck size
The cards remaining face-down. The closed-deck expected value of a random card is the probability of the missing card you need, multiplied by its contribution.
The pick-up decision
The pick-up decision compares two expected values:
- Pick-up value. The probability that the open-pile card improves the hand, multiplied by the contribution.
- Closed-deck value. The probability of any missing card in the closed deck, weighted by the contribution of each missing card.
Example
Open pile shows a 7♠. Your hand has 5♠, 6♠, 8♠, 9♠ (potential run with a 7♠). 5 other spades are visible. There are 8 spades still invisible. The probability of drawing another 7 of any suit or any spade connector that completes a different run is roughly 22% at a 30-card closed deck.
Discard masking
The complementary decision is what to drop after the pick. The desk recommends dropping the highest deadwood in the hand first, on the assumption that the cost of carrying the card is highest at high deadwood values.
Discipline
Discard-masking discipline rewards pre-commitment: at the start of the hand, decide how many of your discards will be high-value deadwood, and stick to that number regardless of the table's read.