What the solution book knows and where it still differs

What it is

43 stack depths from 1 to 100 BB, 8-max tournaments, 12.5% ante from each player (1 BB in total), chip EV. It is our own approximation of an equilibrium: the preflop tree is solved, and what happens after a call is a model, not a full postflop solution. It is not an exact solve and we never call it one. At short stacks the model deliberately values the pot a little differently from strict chip EV, which makes calls and small-blind shoves tighter.

What is calculated directly, and what is not

• 1–5 BB: push/fold ranges come from our own multi-player calculation (every player behind can call, sampled deals, averaged over many iterations), not from the book. Since 29 Oct 2026 the model values the pot a little differently from strict chip EV, on purpose, so it is not a pure chip-EV equilibrium: the big blind calls all-ins less often and the small blind shoves fewer hands. Values are sampled estimates (about 3 points per hand), so treat it as our own calculation, not an exact solution.
• Your hands: hand histories you upload for review are processed in your browser and never leave it.
• ICM trainer and calculators: the Malmuth-Harville model is computed exactly for the stacks and payouts you enter.

What we measured

• 1–5 BB, book vs our calculation: at 4 BB the book plays fewer hands from early position (UTG 26 % vs 29 %) and more from the button and the small blind (button 50 % vs 48 %, small blind 85 % vs 78 %).

Where it still differs

• At most three players in a pot: once three players are in, a fourth can only fold. A very strong hand behind a raise, a 3-bet and a call would really continue; the book does not model that yet (the tree is about four to ten times bigger with four players).
• The small blind jams too often and raises too rarely at 10–30 BB; at 100 BB it limps a little more than a full solution would.
• The opener goes all-in too often against a 3-bet at about 30 BB instead of calling.
• Big blind defence against a small-blind raise is a bit too loose on all-ins and too tight on calls at 30 BB.
• The button opens slightly less than it should at 50–100 BB.
• At 10 BB and below the book keeps min-raises with a few premium hands (a trap) and some blocker hands; the rest jam or fold. This is deliberate, but a full postflop solution may choose differently.
• The big blind against a small-blind limp goes all-in too often at 6–10 BB.
• Anything after the flop in Full Hand is a model estimate, labelled as such.