Guide
Why solver output does not fit the game in front of you
Solver output is not wrong. It is an answer to a question, and the question is what cannot be exploited by an opponent who is also unexploitable. Sit down in a straddled live game with a limper in front of you and almost nothing about that question still describes the hand you are in.
The stacks are not the stacks
The chart in your phone was solved 100 big blinds deep, with an open of 2.5 blinds and one caller. The live version of the same hand has a straddle in it, two callers instead of one, and an opening raise sized for the money already in front of you. What comes out the other end is a different game.
| The hand | Effective stack | Pot on the flop | Players | SPR |
|---|---|---|---|---|
| Solved: 100 bb, no straddle | 100 bb | 5.5 bb | 2 | 17.7 |
| Live: $2/$5 with a $10 straddle | $1,500 | $202 | 3 | 7.1 |
The last column is the one that decides how the hand plays. At the solved ratio it takes 4 pot-sized bets to get a stack in, and there are only three streets after the flop, so the money is never all going in and every street is about position and information. At 7.1 it takes 3, which is exactly the streets available: bet the flop, bet the turn, and somebody is all in by the river whether they planned it or not.
The bluffs assume somebody is defending
An equilibrium strategy bluffs at the frequency that makes an opponent indifferent. That is a defensive property: it stops a good player from beating you, and it is worth exactly nothing against a player who was never going to fold. A bet of half the pot has to work 33.3% of the time to break even, and the solve gets there by assuming the other side folds at the rate that keeps it honest. Nobody at a live table has agreed to that.
Against one opponent who folds too much, the correct answer is to bluff far more than the solve does. Against one who folds too little, the correct answer is to stop bluffing almost entirely. The equilibrium sits between the two, which means it is the right answer to neither.
And there are three of them, not one
Every fold has to happen at once. If each player behind you folds independently, a bluff into three of them needs all three to cooperate, which is the same number multiplied by itself three times.
| Each player folds | One opponent | Two opponents | Three opponents |
|---|---|---|---|
| 50% | 50% | 25% | 12.5% |
| 60% | 60% | 36% | 21.6% |
| 70% | 70% | 49% | 34.3% |
| 80% | 80% | 64% | 51.2% |
Read that against the 33.3% a half-pot bluff needs. One opponent folding 60% of the time is a bet that prints money. The same three opponents fold together 21.6% of the time, and the same bet is now setting fire to it. This is the arithmetic behind every piece of live advice that sounds old-fashioned: bet for value, give up multiway, and stop trying to move four people off a pot at once.
That calculation flatters you, too. It treats the three decisions as unrelated, when in truth a board that gives one player a reason to continue tends to give all of them one.
What does survive the trip
Plenty. Which hands want to be in a raised pot and which do not. How equity runs between a made hand and a draw. Why position is worth more than most people price it at. Which boards favour which range, and why the player who raised first has an advantage on some flops and none at all on others. Those are properties of the cards, and cards do not know what stakes they are being dealt at.
What does not survive is the output itself: the frequencies, the mixed strategies, the precise sizes. Those are answers to a question about opponents you are not sitting with. Take the reasoning and leave the percentages.
Questions people ask
So studying solver output is a waste of time?
No. It is the best available answer to what an opponent cannot punish, and knowing it stops you from being the one who gets punished. It is just not an answer to what makes the most money against the eight people at your table on a Friday night.
Can I not just solve the spot I actually had?
You can, and the answer is exactly as good as the ranges you typed in. The range a live player turns up with after calling three streets is the one thing the solver cannot work out for you, and it is the input that decides the output.
What about the preflop chart, at least?
Which hands to play holds up well. The sizes do not, because they are written in big blinds for a game with no straddle and nobody limping in front of you.
Read next
- How a straddle changes your opening sizesA $10 straddle is the live big blind. Open four of those first in, and two and a half more for every limper, with the real numbers for a $2/$5 game.
- What the rake actually does to your marginal handsA capped drop takes far more out of a small pot than a big one. The real numbers for a $2/$5 game, and what an hour of it costs your win rate.
- What actually beats you when the board pairsTrip eights on the board are everybody's trips. The exact count of the hands that beat you, worked out against every combination left in the deck.
Driller deals the game you sit in: eight-handed, straddle on, limpers in front of you, and the stack you actually buy in for. Then it grades the decision against that table rather than against an equilibrium nobody at it has agreed to play.