Addition is won by chaining gap moves into row runs, not placing one card at a time.

How Addition works

Addition (also known as Gaps or Addiction) deals all 52 cards face-up into four rows of 13. The four Aces are removed, creating four gaps. A gap is filled by the card one rank higher in the same suit as the card immediately to its left: a gap to the right of 5♥ can only receive 6♥. No card can be placed to the right of a King (rank 13 has no rank 14 above it).

When no useful gap-fill exists, a redeal reshuffles all correctly-placed cards out of position and re-deals the scrambled cards back into rows, creating new gaps. Up to three redeals are allowed. Win when all four rows read 2 through King in the same suit.

The gap as a routing resource

Each of the four gaps is a routing resource. Moving a card into a gap consumes that gap’s current position and creates a new gap where the card came from. The chain of new gaps created by each move is the game’s central mechanic.

A gap has value when:

• Its left neighbor determines a specific needed card (the next rank up in that suit).
• That needed card exists somewhere in the layout.
• Moving that card here shifts the gap to a position where another needed card can follow.

A gap is dead when:

• It is immediately to the right of a King (no rank 14 can fill it).
• Its left neighbor’s next-rank card has already been placed correctly in another row.
• Its left neighbor is the last card of a completed run (the King position at end of row).

Chain planning: think three to five moves ahead

Before making any gap fill, trace the chain it starts. Moving a card into gap A creates gap B where that card came from. What can fill gap B? Moving that card creates gap C. Does gap C accept something useful, or does it land next to a King?

The full chain from a single gap move can either:

• Build a complete partial row (high value — multiple correctly-placed cards at once).
• Shift dead gaps to less harmful positions (neutral).
• Create a new dead gap by landing the gap chain next to a King (negative — avoid).

Row strategy: focus completion efforts on one or two rows

With four rows to complete and only four gaps, trying to advance all four rows simultaneously is inefficient. The gap resource is too limited for broad-front progress.

The more productive approach: identify the one or two rows that are closest to completion or that have the longest existing correctly-placed run at the left end. Concentrate gap moves to extend those runs to King. Once a row is complete, the four cards in its final position (ending at King) act as anchors, and the remaining three gaps serve the remaining three rows.

Row selection criteria:

1. The row with the longest existing run from the left (most consecutive correctly-placed cards starting from position 1 of the row, from 2 upward in suit order).
2. The row whose next needed card is most accessible in the current layout.
3. The row whose run, if extended to King, would create the fewest new dead gaps as a side effect of the chain moves.

Redeal timing: when to shuffle

A redeal shuffles all cards not currently in a correctly-placed position and re-deals them. Cards in correct positions stay. This means:

• The more cards correctly placed before a redeal, the fewer cards are scrambled.
• A redeal with only one or two cards placed is a nearly-full shuffle with minimal benefit.
• A redeal with twelve or more cards correctly placed is a small shuffle with high probability of creating useful new arrangements.

Trigger a redeal when:

• All four gaps are dead or effectively stuck (no chain from any gap produces useful placements).
• The ratio of correctly-placed cards to remaining cards is high enough that a redeal will mostly affect a small number of problematic cards.

Avoid redealing impatiently when gaps still have useful chains available. With only three redeals, spending one early when progress is still possible is a significant resource waste.

King management: avoiding dead gaps

Kings end rows. A gap immediately to the right of a King is permanently dead until a redeal changes what is to the left of that gap. Because Kings are the most likely source of dead gaps, King positions throughout the layout matter:

• A King at the far right of a row is ideal — it finishes the row and creates no dead gap within the row (the gap would be at position 14, which doesn’t exist).
• A King in the middle of a row creates a dead gap to its right, effectively reducing that row’s useful length.

When gap chains would land a gap next to a King, trace whether an alternative chain exists that avoids that outcome. Not every dead gap can be avoided, but choosing between equally-legal moves should prefer the option that avoids creating a King-adjacent gap.

How Addition games collapse

• Filling gaps one card at a time without tracing the chain. Single-card gap fills that do not start or extend a run are low-value moves. Always trace the chain a gap fill creates before committing.
• Redealing before extracting maximum value from current gaps. Three redeals sounds like plenty, but games often need all three. Each premature redeal is a wasted shuffle.
• Trying to advance all four rows simultaneously. Four gaps cannot efficiently move all four rows. Focus on one or two rows to completion before spreading gap resources across the whole board.
• Moving a card into a gap without checking whether the new gap position is adjacent to a King. This is the most common way to create an avoidable dead gap. Before each move, check what will be to the left of the new gap position created by the move.