You and a rival each split the same army across three fronts; on each front, more troops wins it, and whoever takes the MAJORITY of fronts wins the war. Spread thin and a concentrated foe overruns two fronts; mass everything and you abandon the rest. There is no safe split — every allocation can be beaten by the right counter. Slide your deployment against an even enemy.
Colonel Blotto: two players each allocate the same total force (100) across N fronts (here 3); each front goes to whoever commits MORE there, and the war is won by taking the majority of fronts. It is a game of concentration versus coverage — against an even split (34,33,33) you win the war by beating it on two fronts, e.g. (35,34,31) takes fronts 1 and 2 while sacrificing 3. Famously, Blotto has NO pure Nash equilibrium: whatever you commit to, a best response can beat it — the essence of feint and misdirection. A fail-loud self-check throws unless a targeted allocation wins the majority against the even split. ◆ real game theory, node-verified.
A 3-front, equal-budget Blotto vs a fixed even opponent (the exact majority-of-fronts rule and the beat-the-even-split result); the full mixed equilibrium is complex and the no-pure-equilibrium property is the deep point — here shown as ‘every split is beatable’.