Benchmarks & research

Abstraction strength and open ranges

Configuration: the lab tree above (3-max, 50bb, no rake), same seed and 4,000 samples each. It compares the small and high abstraction levels. Metric: the SB's unopened strategy in %, and the displayed convergence measure in bb per hand.

	fold	limp	raise	regret bound (bb/hand)
target, 4,000 samples	33.5	40.3	26.3	0.086
small, 4,000 samples	34.4	39.3	26.3	0.086

SB unopened strategy by abstraction strength

high abstractionsmall abstraction

Same tree and samples; the preflop answer moves by about one point.

The regret bound was the same, the big blind's total 3-bet frequency against the SB was the same (14.0%), and every defence node agreed within about one point. The composition of that 3-bet range differed more: the share of hands outside a published reference range was 25% with target and 29% with small. On this tree, at this sample count, strength changed the preflop answer only a little.

This does not show that the abstraction is faithful. Both runs are measured inside their own abstraction, which cannot see abstraction error, and neither was run to convergence. Choose the strength for the postflop detail you want. The first solve at a new strength level builds its cache, which takes a few minutes.

Scope: one 3-max tree at 50bb without rake, one run each. We have not repeated this comparison at other stacks, with rake or with 6 players, and it says nothing about postflop accuracy.