Benchmarks & research

PulseGTO vs PioSOLVER: accuracy, time and memory

Public comparison tables and charts are below. These tests were performed by PulseGTO; they are not a third-party review or a general speed ranking. For preflop comparisons see PulseGTO vs GTO Wizard and HRC; for a full-game training run see the 6-max 100 bb benchmark.

What each engine has been checked against

The preflop engine is the one that approximates: it groups hands and boards and samples the game. Its own accuracy figure measures the game it trains, so the error of the grouping shows only against exact re-solves and outside references like these.

Configuration of the flop trees: heads-up postflop, 100 chips effective, pot 10, rake 5% capped at 3. Bets are 33% and 75% of the pot on the flop and turn, and 33%, 75% and 125% on the river. Donk bets are 33%, raises 75%, and all-ins follow the reference's rules (threshold 67%, extra all-in only when the stack is at most 5× the pot). The same two ranges were used throughout. The reference's own tree file (366 lines) is rebuilt by PulseGTO line for line, with identical bet amounts. Exploitability is the reference's "Exploitable for": the average over both players of (best response − EV), in chips.

Step by step: river and turn trees

Five small trees on Qs Jh 2h 7c (3d), pot 10, 1,000-chip stacks except step 5, each adding one rule, solved to convergence by both solvers. EV in chips, OOP / IP.

Step 5 differs by 0.003, which is within the reference run's own exploitability (0.006). Steps 1 to 3 were also checked against an independent exact river solver.

Full flop trees

The EVs agree to within about 0.015 chips. That is less than the exploitability of the solutions themselves, so the remaining difference is convergence, not a different game. The expected rake agrees as well: 0.95 to 0.96 chips on Qs Jh 2h and 1.19 to 1.20 on As 9h 4d.

Flop strategy

170 of the 183 OOP combos are within 5 points of the reference's PIO_CFR run. The largest differences are hands that mix bet and check at almost equal EV, such as KdTc (check 45% vs 56%) and KcTc (17% vs 0%). The two reference algorithms disagree on the same kind of hand: KdTc checks 56% in one and 52% in the other.

Qs Jh 2h is harder to compare hand by hand. OOP almost never checks, and splits its bets between 33% and 75% of the pot, two sizes of nearly equal value. Over the whole range the results agree: PulseGTO bets 33% 75.3% of the time and 75% 24.7%; the reference's original algorithm bets 72.5% and 26.8%, and checks 0.7%. Per hand, though, the two differ by 10.8 points on average. The reference splits a hand such as Ac Qh 39/60 between the two sizes, while PulseGTO splits it 87/13. Two independent PulseGTO runs agree with each other to within 0.1–0.8 points per hand. So each program settles on its own split between two sizes that are worth almost the same, and both split with the same total value: the EVs agree to 0.01 chips.

EV of every combo

A turn spot, As 9h 4d 9c: pot 10, 100 chips effective, rake 5% capped at 3, bets 33% and 55%, raise 75%, donk 33%, 77 OOP combos against 51 IP combos. Both solvers were run to about 0.001 chips of exploitability.

Over the 77 OOP combos the EVs differ by 0.0005 chips on average and by 0.005 at most. At the root, the check frequency differs by 0.44 points per combo on average and by 2.3 at most.

Time and memory, for context only

Time until a check first showed each exploitability level or lower, in chips. A check happens only every 30–60 s, so each figure can be up to one interval late. A dash means the level was not reached before the run was stopped.

Both programs use suit isomorphism. It removes about a quarter of the work on a two-tone flop such as Qs Jh 2h and nothing on a rainbow flop such as As 9h 4d, which is why both need more time there. Memory is measured differently for each program, so compare it only roughly.