Batch mcts-m2. Model 0.1.0, graph 0.2.0, parameters 0.1.0. 50 simulations, seeds 1 to 50; 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, 50 times. Its capability index moved from 16.45 to a median of 18.28 (+1.83), with 90 per cent of simulations between 17.80 and 18.62 [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 951 credits a year, calibrated so that its 2026 position is affordable with headroom for investment.
What was decided
A simulation spent a median of 3,676 credits on actions. The five groups that took most were Foundational Education (build, 142 credits, 3.8 per cent); Lifelong Learning & Reskilling (build, 135 credits, 3.6 per cent); Technical & Vocational Skills (build, 127 credits, 3.4 per cent); Early Childhood Development (build, 118 credits, 3.2 per cent); Transparency, Oversight & Accountability (build, 116 credits, 3.1 per cent) [experiment_decisions_by_group]. By mode: build 41 per cent, partner 35 per cent, buy 24 per cent [experiment_decisions_by_group]. Concentration of spending (HHI) had a median of 0.025, 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, Governance & Integrity; 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 92 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 S03 (19 firings in 18 simulations, −22.8 points each); S09 (5 firings in 5 simulations, −22.3 points each); S01 (12 firings in 10 simulations, −20.3 points each) [experiment_shocks]. Upside events fired 66 times across all simulations [experiment_shocks].
The groups that lost most to shocks, per simulation: Fiscal Capacity & Public Finance −1.13; Economic Leverage & Dependence −1.06; Trade Facilitation & Logistics −1.01; Investment Attraction & Projection −0.98 [experiment_shock_damage_by_group].
The edges that carried most change through the graph, per simulation: Economic Output & Productivity to Fiscal Capacity & Public Finance (+0.55 points); Foundational Education to Advanced Education (+0.62 points); Advanced Education to Research Talent & Knowledge Creation (+0.50 points) [experiment_propagation_by_edge].
Where it ended
At 2046 the median rank is 1 (5th to 95th percentile 1 to 2), the median count of Tier 1 domains 7 (6 to 7) and the median tier rank 2; the resilient score, the mean score sum over simulations, is 1,325 [experiment_objectives].
Tier 1 probability changed most in: financial strength (0 to 100 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 88 per cent of simulations); trade and investment (0 to 100 per cent of simulations) [experiment_tiers_by_round].
Why
Without shocks the index ends +0.147 higher on average, so the shocks cost about 0.147 index points [experiment_probe_attribution].
Holding instead of following this method changes the index by −1.989: 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 −0.010, for example 2046 partner Sovereign Capital & External Financial Power (54 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 +0.083 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
move_without_shock (warn): largest one-round change in a group with no shock landing: 3.39 points; 78% of simulations have one above 3.
saturation_high (warn): 96% of simulations end with a group at 20 that did not start there (median 8 groups).
indifferent_search (warn): in a median simulation the top two root candidates were within 5 per cent of visits in 100 per cent of rounds.
The simulation furthest from the median (seed 33) ends −0.76 from it, with 7 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 tier_rank (minimised, so negated in the search); playouts drew their futures from the stochastic scenario.
The committed decision most often chosen, round by round: round 1 greedy (28 per cent of simulations, visit share 5 per cent); round 2 greedy (34 per cent of simulations, visit share 5 per cent); round 3 greedy (22 per cent of simulations, visit share 5 per cent); round 4 greedy (32 per cent of simulations, visit share 5 per cent); round 5 greedy (36 per cent of simulations, visit share 5 per cent) [mcts_decision_sequence]. The search hesitated (top two root candidates within 10 per cent) in 100 per cent of decisions, considered a mean of 30 candidates, grew trees of a mean 427 nodes to depth 3.8, and took 1.3 seconds a decision [mcts_decision_sequence].
Where the committed actions came from, by proposing generator (committed simulation-rounds): marginal return 26.0; greedy 6.2; goal gap 4.9; graph leverage 2.9; graph leverage | marginal return + graph leverage 1.4 [mcts_root_candidates].
Against the greedy experiment with the same seeds (m2-gbr-greedy-marginal), the search's tier_rank at the horizon is 0.000 on average (10th to 90th percentile 0.000 to 0.000), better in 0 per cent of seeds; on the index −0.024, the score sum −1.0 and Tier 1 domains −0.04 [mcts_regret].
Across seeds the same root decision won in a mean 31 per cent of simulations (first five rounds 30 per cent) [mcts_stability].
The principal variation was followed 100 per cent at depth 1, 20 per cent at depth 2, 31 per cent at depth 3, 29 per cent at depth 4 [mcts_pv_vs_path].