From Blades in the Dark: There are two easy ways to get an extra die when making a check, both of which cost Stress, the finite do-cool-stuff resource pool for the game.
If you're going solo you can use Push Yourself, which grants you an extra die. If someone's assisting you, they can use Help, which gives someone else an extra die.
Where it encourages teamwork is in the cost - Push Yourself costs 2 stress, while Help only costs 1.
Outside of
@Blue 's 4e Marking and Defender suites (forcing catch-22's on Team Monster which either protects allies, sets up allies, or punishes enemies), this is the first one that came to mind for me.
The other two in Blades that encourage
Teamwork are:
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Leading a Group Move: One Teammate leads and assumes the Stress Liability if any group member (including themselves) rolls a 1-3 (1 Stress per 1-3 dice pool result). Each PC rolls their dice pool, top result among the group stands.
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Setup: Increase Position (consequence severity) or Effect (what you can accomplish with an Action Roll) by setting your ally up.
Torchbearer has similar where you're
Helping (add +1d6 to teammate dice pool) either via using the same Skill as primary, an associated Skill, a Nature Descriptor, or a Wise. If you spend a metacurrency, you can mark an advance (pass or fail depending on the result) with the Skill. Further, if you're able to use a Wise to Help, you insulate yourself from fallout if the result is a "Failure as Success but Condition (you don't get a Condition)."
Dogs in the Vineyard has similar in its Conflicts where you
Lend a dice to an allies Dice Pool. Probably the most important aspects of winning the stakes of Dogs' Conflicts is (a) getting and avoiding Reversing the Blow and (b) knowing when to Escalate. Well-played use of Lending will enable allies to Reverse the Blow.
Things in games that encourage
Soloing or
Splitting the Party are the following:
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Broadly-competent, robust, resourceful, and resilient PCs (either through PC build dynamics or other system tech/principles). Dogs features this, Blades features this, Dungeon World and Stonetop features this.
You can also build toward this in 4e with capable Striker builds or beefy Controllers with Multiclass Feats to increase breadth-of-Skills + 2 Utilities and/or Skill Powers devoted to calling upon Healing Surges as Minor/Free Actions at the Encounter level (Bladesingers, Duelist Rogues, Barbarians, Monks, Swarm Druids, Slayers). This can also be accomplished with a Companion Character alongside the "solo" PC (a Companion Character doesn't have to be a tangible thing...it might be a spirit or a sense of purpose/conviction or display of prowess merely stated up as a CC and given position and action economy). Encounter budgets work beautifully regardless of how many PCs are in the group so a Level +2 Encounter works different for a Solo fight than it does with 3 PCs (because the budget works off of the # of PCs).
* Having a
"Home Base" as the nexus of play and having multiple Opportunities and/or Threats to pursue or resolve. Apocalypse World, Blades in the Dark, Stonetop, and The Between works off of this model. One PC or a team of 2 PCs pursues a small Score here in Blades while the other 1 or 2 perform another small Score. Same thing in the other games but it has nomenclature different from Score.
The point is the play loop centers around a physical nexus, a shared home base (a Steading like Stonetop, the Hardholder's stronghold in AW, The Crew's Lair in Duskvol, Hargrave House in Fantasy Victorian London in TB). We improve our standing and we head off trouble and the best way to do that is to pursue multiple agendas simultaneously while allocating resources accordingly. The GM just cuts back and forth between PCs/Split-parties.