Batch mcts-m2b. Model 0.2.0, graph 0.2.0, parameters 0.1.1. 20 simulations, seeds 1 to 20; probes on 5. Every figure is a distribution over simulations of a structural model with seed parameter values; it shows what the model implies under these settings, not what will happen. Other nations are frozen at their 2026 ratings. No reconstructed historical data is used in this experiment.
Headline
United Kingdom played 20 rounds from 2026 under the tree search (mcts) method, with stochastic events, 20 times. Its capability index moved from 16.45 to a median of 17.93 (+1.48), with 90 per cent of simulations between 17.17 and 18.69 [experiment_objectives].
Starting position
In 2026 the nation ranks 3 on the index against the frozen field, holds 2 of nine domains at Tier 1 and has a tier rank of 5. Its base income is 1,094 credits a year, calibrated so that its 2026 position is affordable with headroom for investment.
What was decided
A simulation spent a median of 3,072 credits on actions. The five groups that took most were Diaspora & Global Communities (build, 90 credits, 3.0 per cent); Technical & Vocational Skills (build, 85 credits, 2.9 per cent); Economic Output & Productivity (build, 83 credits, 2.8 per cent); Early Childhood Development (build, 83 credits, 2.8 per cent); Lifelong Learning & Reskilling (build, 82 credits, 2.8 per cent) [experiment_decisions_by_group]. By mode: build 48 per cent, buy 28 per cent, partner 24 per cent [experiment_decisions_by_group]. Concentration of spending (HHI) had a median of 0.024, and the most repeated action appeared in 15 per cent of rounds.
The leading domain by period: rounds 1 to 5, Human Capital; rounds 6 to 10, Trade & Investment; rounds 11 to 15, Governance & Integrity; rounds 16 to 20, Critical Technology [experiment_spend_by_period].
The method's chosen action was within 5 per cent of its best alternative in 99 per cent of actions and ahead by more than 25 per cent in 0 per cent [experiment_decision_margins].
What the world did
A median simulation saw 2 shocks and 1 upside events. The most damaging per firing were S09 (3 firings in 3 simulations, −24.2 points each); S03 (10 firings in 9 simulations, −22.4 points each); S08 (12 firings in 11 simulations, −21.2 points each) [experiment_shocks]. Upside events fired 25 times across all simulations [experiment_shocks].
The groups that lost most to shocks, per simulation: Fiscal Capacity & Public Finance −1.32; Economic Leverage & Dependence −1.16; Trade Facilitation & Logistics −1.15; Digital & Services Trade −1.15 [experiment_shock_damage_by_group].
The edges that carried most change through the graph, per simulation: Economic Output & Productivity to Fiscal Capacity & Public Finance (+0.49 points); Foundational Education to Advanced Education (+0.50 points); Fiscal Capacity & Public Finance to Social Infrastructure (+0.29 points) [experiment_propagation_by_edge].
Where it ended
At 2046 the median rank is 2 (5th to 95th percentile 1 to 2), the median count of Tier 1 domains 6 (5 to 7) and the median tier rank 2; the resilient score, the mean score sum over simulations, is 1,302 [experiment_objectives].
Tier 1 probability changed most in: financial strength (0 to 90 per cent of simulations); human capital (0 to 100 per cent of simulations); information and influence (0 to 100 per cent of simulations); strategic infrastructure (0 to 50 per cent of simulations); trade and investment (0 to 100 per cent of simulations) [experiment_tiers_by_round].
Why
Without shocks the index ends +0.296 higher on average, so the shocks cost about 0.296 index points [experiment_probe_attribution].
Holding instead of following this method changes the index by −1.885: that is the method's worth against doing nothing [experiment_probe_attribution].
Removing any single one of the five largest actions changes the index by between −0.023 and −0.015, for example 2039 partner Space Technologies (36 credits) [experiment_probe_attribution]. The largest actions by credits come late, when income is highest, and are rarely the most valuable.
Removing the largest shock of a simulation raises the index by +0.166 on average [experiment_probe_attribution].
The replay probe reproduces the simulations exactly (index change 0.000000), so the attributions are clean [experiment_probe_attribution].
Surprises
saturation_high (warn): 90% of simulations end with a group at 20 that did not start there (median 2 groups).
The simulation furthest from the median (seed 8) ends −1.19 from it, with 6 shocks and 0 upside events [experiment_outlier_simulations].
Comparison
This is the baseline (hold) experiment, or there is none for this nation in the batch.
No backcast comparison: this experiment does not start from a historical position [experiment_against_history].
The search
Monte Carlo tree search 0.1.0 with candidate generators 0.1.0 (marginal return, graph leverage, goal gap; top 4 groups each), 500 iterations a decision, UCT c = 1.4 scaled to the reward spread, widening alpha = 0.5, greedy playouts to the horizon, objective index; playouts drew their futures from the none (certainty-equivalent playouts: the planner ignores shocks) scenario.
The committed decision most often chosen, round by round: round 1 hold (65 per cent of simulations, visit share 57 per cent); round 2 hold (35 per cent of simulations, visit share 34 per cent); round 3 hold (25 per cent of simulations, visit share 29 per cent); round 4 hold (50 per cent of simulations, visit share 40 per cent); round 5 build Fiscal Capacity & Public Finance (30 per cent of simulations, visit share 49 per cent) [mcts_decision_sequence]. The search hesitated (top two root candidates within 10 per cent) in 43 per cent of decisions, considered a mean of 34 candidates, grew trees of a mean 436 nodes to depth 4.9, and took 0.9 seconds a decision [mcts_decision_sequence].
Where the committed actions came from, by proposing generator (committed simulation-rounds): marginal return 28.6; greedy 4.3; goal gap 3.2; hold 2.3; graph leverage | marginal return + graph leverage 1.6 [mcts_root_candidates].
Against the greedy experiment with the same seeds (m2b-gbr-greedy), the search's index at the horizon is −0.042 on average (10th to 90th percentile −0.227 to +0.207), better in 30 per cent of seeds; on the index −0.042, the score sum −3.0 and Tier 1 domains −0.35 [mcts_regret].
Across seeds the same root decision won in a mean 33 per cent of simulations (first five rounds 41 per cent) [mcts_stability].
The principal variation was followed 100 per cent at depth 1, 43 per cent at depth 2, 26 per cent at depth 3, 24 per cent at depth 4 [mcts_pv_vs_path].