ICM (approximation, MTT only): payouts to 15% of the field, ICM (Malmuth-Harville). A player's stack (in the menu next to the profile: short = half the average, average, big = double) changes how much a loss against the opponent costs him and how the opponent answers; the stack picked on the left is the effective stack of the hand. Every preflop action is converted from chips to its ICM value and the strategy shifts by the difference. On the turn and river the solver works with ICM directly (each player with his own curve); on the flop ICM raises the equity needed to call and adds a few bluffs. It is not an exact ICM solution: the direction is right, the size is an estimate.

Preflop comes from a preflop solver solution (chip EV, 8-max, ante 1 BB in total; up to 35 BB open 2 BB and from the SB 3 BB or limp, from 40 BB open 2.3 BB and from the SB 3.5 BB; 3bet 2.5× in position and 3.3× from the blinds, all-in when the bet is over 40% of the stack). For every stack it is a separate solution of the whole preflop, including cold calls, squeezes and multiway pots. Postflop the app plays heads-up only: when three players see the flop, the hand stops there. The range on the flop is, for every hand, the product of the shares of the actions the player chose preflop. Hands you repainted are applied on top.

Player profiles: range tight / loose narrows or widens every action that puts money into the pot to 0.75× or 1.35×; aggression passive / aggressive shifts the ratio of raises and calls (raises 0.6× or 1.5×, the rest as calls). Hands are added and removed by their EV in the solution. Postflop a loose player continues against a bet with 2 times more of his range than a balanced player and a tight one with 0.6 times as much; against a loose player the app therefore bluffs less and value bets thinner, against a tight one it bluffs more (verified by simulation against calling-station, nit and maniac bots); an aggressive player has more air in his betting range and a passive one less. The sliders at a decision take precedence over the profile, repainted hands over both. The “Next” button (it shows when someone has a profile) starts the next hand at the same table: the button moves one seat and the profiles move with the players (SB → BTN, BB → SB, BTN → BB; heads-up they swap). “New” starts from scratch and clears the profiles.

When an opponent has a different profile (or an edited strategy), the player facing his raise or limp adapts to him: the EV from the preflop solution stays the base, and our model adds the change caused by the opponent's different range and his different reactions to a 3bet or all-in (fold, call, re-raise), computed from preflop equity. Half of this change is counted, because the opponent would partly adapt too and the model doesn't see all the costs of the new line (for example playing out of position). In the same way the player who enters the pot first (open, limp, all-in) adapts to the players behind him: it counts how often everyone folds and what the one who continues does. Such a card has “vs” and the opponent's name in its header. When everyone is GTO, the strategy is exactly the preflop solution.

At every step the calculation is for the player to act: the equity of each of his combos against the opponent's current range, exact on the turn and river, simulated on the flop (±1.5 points). For every combo the EV of all options is compared and the best one is chosen.

A bet or all-in assumes the opponent continues with his strongest hands, roughly enough of them for a pure bluff to break even (for a bet B into a pot P that is the share P ÷ (P + B)), 0.8 to 1.2 times that depending on the assumption; for a flop c-bet another 0.8 times, because according to the solver the range of the player who called preflop folds more there than MDF would suggest (many hands don't have enough equity). The strength of his hands is measured by how often they beat the range of the player to act right now; draws get a bonus. Hands that beat most of that range never fold. For bets above half the pot this threshold goes up, because a big bet comes from a stronger range: against a pot bet a hand must beat about 60% of the range, against an all-in for twice the pot about 72%. A weak pair and draws therefore often fold against a big bet and call a small one. All-in is offered only with an SPR up to 3.

The player out of position realizes less equity (by default draws 80%, made hands 92%), the player in position all of it. Realization does not apply on the river.

When you click an action, the player's range narrows. After a bet, the hands that chose exactly this bet stay whole, hands with another size stay with weight 35% and checking hands with weight 25%. After a check, the hands that chose the check stay whole, and those that would have bet stay with weight 85%, because strong hands often check for a check-raise or a slowplay. These “mixed-in” hands can make up at most 15% of the range after a bet and 25% after a check: when an action is rare (e.g. a river all-in from a fifth of the range), a fixed weight would turn the checking hands into half of the jamming range and the opponent would call much wider than he should. After a call, the hands that should have folded are removed. A raise counts as a bet the other player faces, with both previous bets in the pot.

Postflop is calibrated to the average flop frequencies of solver solutions with bets of ¼, ½, ¾ and pot in 18 situations (BTN–BB, CO–BTN, UTG–BB, SB–BB, limped pot, 3bet pot; 20, 40 and 60 BB). On a bet the model assumes the opponent raises part of his continuing hands (a quarter; strong hands plus bluffs) and the bettor then continues only when it pays. A check on the flop is worth 25% less (in position) and 60% less (out of position, the player gives up the initiative), in a limped pot out of position 40% less and in a 3bet pot 50% less, on the turn 30% less; weak hands realize less equity, the player in position 95%. Against a bet you can raise to 3× the bet (at least half the pot more) or go all-in. The average deviation from the solver is 6–9 points by pot type; the exception is a raise with the aggressor out of position (CO against BTN, about 15 points), where the BTN with a narrow and strong range folds less to a bet than in the solver solution.

Range advantage on the board: on the flop, the equity of the range of the player to act on this board is compared with the equity of the same ranges before the flop (i.e. on an average flop). When the board helps him, the opponent defends a bit tighter against a bet and raises less (up to 70% less); when the board helps the opponent, he defends wider and raises more often (up to 3 times). The average over all flops stays the same as in the solver calibration. It measures equity, not just the share of the strongest hands, so who has more sets and straights on the board is only partly taken into account.

Balanced bluffs: against an opponent who defends in a balanced way, a pure bluff would break even and the model would bet only value. The solver, however, keeps bluffs in its betting range so that the opponent can't fold everything but strong hands. The app therefore adds bluffs to a bet at roughly B ÷ (P + 2B), 2 times more on the flop and 1.5 times more on the turn (bluffs can still improve). Draws (semi-bluffs) are taken first, then the weakest hands; hands with medium showdown value check. Against a loose opponent no balancing bluffs are added, only value. Every bet size must also have value: when there would be more bluffs than the bet can carry, the strongest hands that lose little by it move into it and the extra draws check.

One bet size: in every decision the bet is made with one size, the one that earns the most for the whole range (each hand either bets it or checks). When each hand picked its own size, strong hands bet big and medium ones small: the small bet was then “capped” and the solver raised it, the big one was pure value and the solver folded to it. A comparison with a postflop solver on the same ranges (8 flops and 16 turn and river spots, 10–20 BB) showed that together with the other changes the EV loss when the solver punishes the app's strategy fell on the flop from 0.57 to 0.12 BB on average, and on the turn and river by about 60%.

Deep stacks (more than 4 pots behind the bet, i.e. MTT from ~40 BB and 3-bet pots at 100 BB): the model counted the later winnings of a strong hand by the pot the bet creates, so with many chips behind a pot bet came out too good. In a 3-bet pot on A98 or QJT it bet pot where the solver bets a quarter pot, and lost 1.2–1.4 BB per hand. Now a bet adds half of the later winnings and a check keeps 70% of its own; shallow stacks (Spin & Go, MTT up to ~25 BB) don't change. In a test against the solver on 9 flops (40 and 100 BB, single-raised and 3-bet pots) the total loss fell from 5.3 to 1.7 BB. Paired and connected boards in 3-bet pots (884, 765: around 0.4–0.5 BB) remain weaker, where the solver mixes several sizes at once.

A limped pot where the BB is out of position (heads-up, or BTN limp and the SB folded): according to the solver the BB almost never leads the flop and the limper in position bets wide after a check, most often with the minimum bet of 1 BB (½ pot). The app plays it that way too: the BB checks, the SB bets its whole range small. The solver bets 45–80% of the range depending on the board; in a test against the solver the BB and SB lose 0.08–0.11 BB per hand together, previously 0.23–0.29 BB.

A raise against a bet works the same way: strong hands raise to the usual size (3 times the bet) when it is almost as good as all-in, so that the opponent's worse hands stay in the pot. Semi-bluffs are added to them at roughly (raise − bet) ÷ (pot + 2 × raise), 2 times more on the flop and 1.5 times more on the turn, draws first; a bluff can be a quarter pot worse than the best action (balance has its price). Against a ¼ pot c-bet at 20 BB the BB thus folds 43%, calls 34%, raises 18% and goes all-in 5% (solver 40 / 36 / 18 / 5). Against a loose opponent no bluffs are added to raises.

The player without the initiative who is first to act (for example the BB after calling an open) checks to the aggressor; donk bets can be turned on in the assumptions. The initiative belongs to the last preflop raiser and then to whoever bet or raised last; when the aggressor checks behind, he loses the initiative and the player out of position can bet first on the next street. The model doesn't know the implied odds of draws or a smaller raise as its own option.

Future value: when play goes on after a call, a check or a called bet, a strong hand wins part of the stack behind on later streets. It is estimated as (equity − 50%) ÷ 50%, times the smaller of “the stack behind” and “1.5 pots on the flop, 0.75 pot on the turn”; at 50% it is zero, at 100% all of it. After a check it is reduced by the air in the opponent's range, because that pays later only by bluffing: after a check out of position by half the air, after a check behind by all of it. After a call or a called bet it applies in full, because the opponent's bluffs keep betting. Top set with 95% equity at an SPR of 2 therefore prefers to call, because an all-in would chase away hands that would pay it later. It can be turned off in the assumptions. A draw is a combo whose equity is at least 8 points higher than how often it is ahead now; draws have their own realization.