What a solver is, and what it is not
An equilibrium is a different kind of answer from an equity. Here is the difference, and why it matters before you look at one.
6 minute read
Everything so far in this academy is a fact about cards. Given your hand, the board and a range, the equity is a number that nobody can argue with, and every page here shows the count behind it. A solver answers a different question: not how likely am I to win, but what should I do. Its output is a strategy, and a strategy is only right relative to what the other player does.
A solver takes a simplified game as input: two ranges, a menu of bet sizes, a stack depth and a rake. It then plays that game against itself, adjusting both sides, until neither player can gain by changing any decision. The result is called an equilibrium. For every hand at every point in the tree it returns a mix of actions, with a frequency and an expected value for each.
Equilibrium
No hand can raise its EV by changing its action, given what the other player does
That is the whole definition. Nothing in it says 'best against this opponent'; it says 'cannot be exploited by any opponent'.
Exact versus equilibrium
The equities on this site never move. A solver's frequencies move whenever an input moves: give it a wider range or a different bet size and every number on the grid changes. That is not a flaw. It is what it means to compute a strategy rather than a probability.
The mixes are the part that confuses people. A solver will say bet 62%, check 38% with one hand. That is not indecision. It is the exact blend that leaves the opponent no profitable way to adjust, and the mechanism behind it is pot odds turned around, which is the next lesson.
Click a slot to change the board.
Player 1
—Player 1's range
15.0% of hands · 187.2 live combos (11.7 blocked)
Paint the matrix, or type ranges like 22+, A5s+, KTs-K7s, AA:0.5. Enter applies.
Player 2
—Player 2's range
30.0% of hands · 369.8 live combos (28 blocked)
Paint the matrix, or type ranges like 22+, A5s+, KTs-K7s, AA:0.5. Enter applies.
Quick check
A solver bets a hand 40% of the time. Does that mean betting is 40% likely to be the best play?
Show answer
No. At equilibrium the actions in a mix have equal EV for that hand; the frequency is chosen to keep the opponent indifferent, not because one action is 'more right'.