Three-front allocation
Allocate one fixed budget secretly across three independent majority contests.
Logic & rule checking
- Players
- 2 players
- Time
- 12–20 minutes
- Materials
- Six fictional units each, three front cards worth 2,3,4 and five-round log.
Prepare
Place three fronts labelled L worth 2, M worth 3 and R worth 4. Each player has six units each round and must allocate every unit as nonnegative whole numbers across L,M,R. The allocation is written secretly before either is revealed; no borrowing from a later round.
Play
Reveal both triples together. At a front, strictly more units wins that front’s full point value. A tie gives neither player points there, even if both allocated zero. Each round’s points are added to a permanent score. Units themselves do not score and are completely reset for the next round.
Worked example
For allocations (3,2,1) and (1,2,3), the first player wins L for 2, M ties for 0, and the second wins R for 4. A triple(3,3,1) is illegal because it uses seven units, even if its owner would still lose a front.
Finish and check
Play five rounds and compare total points; equal totals draw. If a triple is illegal, hide both allocations again and have both rewrite that round with legal totals so no one gains a free look. Do not redistribute units after seeing the opponent’s row.
Adaptation and limits
Use paper numbers instead of counters, with a partner verifying that each triple sums to six. It is an abstract simultaneous-allocation game, not military advice or spending guidance. Discuss what was sacrificed at one front without labelling a participant by a single choice or claiming a universally winning allocation.
Purpose, observation and provenance
Within this activity: Allocate one fixed budget secretly across three independent majority contests.
Explain one legal decision and check it against the written constraints; a single result does not measure lasting ability.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Three-front allocation
Front L2 / M3 / R4. Each round allocate exactly 6.
Round / L / M / R / sum 6? / points.
Player record · keep host key separate
| Round | L | M | R | Sum/points |
|---|---|---|---|---|
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
Host key · separate from players
(3,2,1) versus(1,2,3) scores 2 versus 4. There are 28 nonnegative integer triples summing to 6.
Run the round
Place three fronts labelled L worth 2, M worth 3 and R worth 4. Each player has six units each round and must allocate every unit as nonnegative whole numbers across L,M,R. The allocation is written secretly before either is revealed; no borrowing from a later round.
Reveal both triples together. At a front, strictly more units wins that front’s full point value. A tie gives neither player points there, even if both allocated zero. Each round’s points are added to a permanent score. Units themselves do not score and are completely reset for the next round.
For allocations (3,2,1) and (1,2,3), the first player wins L for 2, M ties for 0, and the second wins R for 4. A triple(3,3,1) is illegal because it uses seven units, even if its owner would still lose a front.
Play five rounds and compare total points; equal totals draw. If a triple is illegal, hide both allocations again and have both rewrite that round with legal totals so no one gains a free look. Do not redistribute units after seeing the opponent’s row.
Use paper numbers instead of counters, with a partner verifying that each triple sums to six. It is an abstract simultaneous-allocation game, not military advice or spending guidance. Discuss what was sacrificed at one front without labelling a participant by a single choice or claiming a universally winning allocation.
Related activities
Activity library · Shared threshold project: rules and printable materials