Is simplifying poker strategy the road to success? I measured the cost

“Simplify your strategy” is advice everyone gives and almost nobody prices. Solver charts are full of hands that raise 45% of the time and call 55% of the time, and nobody plays that at the table. So what does it actually cost to round it off?

I pulled the solutions out of Poker Academy and measured it. Two different things get called simplifying, and only one of them is expensive.

• Collapsing a mix — playing one action where the solver splits — costs under 0.001bb a hand.
• Carrying one chart into a spot it wasn’t built for costs 0.007 to 0.044bb a hand, up to 1.06bb on a single hand.
• Forcing one bet size on every flop costs up to 0.79bb a flop if you keep the wrong one.

Every number below is measured against an opponent who keeps playing the solver strategy. That makes all of them lower bounds — someone who notices your simplification exploits it further than this. I’ll come back to that at the end.

The solver only mixes between actions it prices the same

Here is the spot I’ll use for the preflop half: NL200 fast fold cash, 100bb, 6-max, no ante. Everyone folds to the button, the button opens to 2.5bb, and the big blind has to decide.

Over all 1,326 combos the big blind folds 59.5% (789 combos), calls 29.0% (384) and 3-bets to 11bb 11.5% (153). Look at the matrix and most of the interesting cells are split in two. JTs is one of them. Click it and the app shows all four combos:

That is the whole answer. The 3-bet is worth +0.69781bb, the call +0.69862bb. They differ by 0.00081bb — less than a thousandth of a big blind.

This is not a coincidence of one hand. It is what a mixed strategy is. The solver splits a hand between two actions only when it values them equally; if one were better it would take that one every time. The split exists to keep the opponent from reading your range, not because the hand is worth more cut in half.

Replace the mix with either of its actions and you keep 0.698bb. There is nothing to lose because there was no gap to begin with.

Collapsing the mix: measured, and it really is free

Poker Academy has a switch for this. In Browse, under Display, turn on Simplify and the same node redraws with the splits collapsed.

I ran the collapse over every hand in the node and weighted it by combos: 6 for a pair, 4 suited, 12 offsuit. Three spots from the same simulation:

• LJ opening, first in: 6.6% of combos are split. Range EV changes by less than 0.001bb a hand; the worst single hand loses 0.0003bb.
• BB against the button open above: 33.5% split. Under 0.001bb a hand, worst hand 0.0010bb.
• BB after a small blind limp, where the big blind can check or raise to 4bb: 80.1% split — four combos in five. Still under 0.001bb a hand, worst hand 0.0094bb.

One detail worth being honest about: in every one of those spots the collapsed chart scores a hair higher than the mix — by at most 0.0004bb a hand. That is not an edge. It is the residual left in the solution because the solver stopped at a small but non-zero distance from equilibrium. If you see a simplification that beats the solver by a thousandth of a big blind, you have found convergence noise, not a leak.

An old claim from the previous version of this post — that the big blind plays 100% of hands after a small blind limp — holds exactly in the solution I pulled: fold is 0.0% of all 1,326 combos, raise 41.8%, check 58.2%.

What the Simplify button actually does

The old description of this feature, and the tooltip in the legacy tournament charts, says it “rounds mixed % actions: 0-33% → 0, 34-66% → 50%, 67-100% → 100%” — that string is still in the app today. It is not the algorithm. I read the source (src/shared/strategy/simplify.ts, the single implementation both the legacy charts and Browse call). It is a pattern match over the whole four-action distribution, not per-action rounding:

• Exactly two actions each above 34%, with the other two each below 10% → those two split 50/50.
• Otherwise the strictly largest action takes 100% and the rest go to zero.
• If neither fits — an exact tie, or a three-way mix like 35/35/30 — the strategy is left unchanged.
• Frequencies are rounded to two decimals before any of that, and the comparisons are strict.

Most of the time the two descriptions agree. Across every named node of three simulations — 1,498,760 combo-instances — they differ on 0.55% of them. On those hands the difference is not cosmetic. 66 opening from LJ in this cash game raises 65.7% and folds 34.3%. Round each action on its own and you get “open half the time”. The app shows a pure open, because 34.3% rounds to 0.34 and the 50/50 rule needs strictly more than that.

I’d rather have the pure open — “open 66 from LJ” is a rule you can follow, “open it two times in three” is a rule you will misapply. But it is worth knowing which one the button gives you.

The expensive simplification: one chart, more spots

Now the part that costs money. The real simplification people make is not “round off JTs” — it is “I have one big blind defence chart and I use it against everybody”.

So I took the simplified big blind chart built against a button open and used it against an LJ open — same simulation, same 100bb stack, same menu of call, 3-bet or fold. Then I priced every hand with the EV table of the spot it is actually being played in.

25.5% of combos get a different action from the two charts, and it costs 0.024bb a hand in that direction, 0.044bb in the other. Two hands show where it comes from:

• J9o — the button chart 3-bets it. Against an LJ open the solver folds it 100%, and 3-betting is worth −0.281bb against 0.00 for folding.
• QQ — the LJ chart calls it, because against an early open the solver calls QQ 69.1% of the time. Against a button open, 3-betting is worth +4.742bb and calling +3.678bb. Flatting costs 1.064bb, every time you do it.

Here is the measurement that settles the argument. If I carry the unsimplified chart — the full 25/75 mixes — into the wrong spot, it costs 0.0243bb a hand instead of 0.0236 — rounding the mix off changes the bill by 0.0007bb, in favour of the simplified chart. The cost is the wrong spot, not the mix.

That also tells you what to simplify first. Collapsing mixes buys a memorisable chart for free; using one chart in five spots buys 25% wrong actions.

Postflop: one size on every board

The spot: MTT, 20bb, 9-handed, 1bb big-blind ante. The button opens to 2bb, the big blind calls. Pot 5.5bb (2 + 2 + 0.5 + 1), 18bb effective. The big blind is out of position, so it acts first on the flop.

The old post said the solver “advises some raising” here about 2.3% of the time. It can’t. The big blind is first to act and nobody has bet — there is nothing to raise. The action is a lead, or donk bet, and the frequency for it is small but real. On K♣︎K♦︎4♥︎ the big blind checks 92.3% of the time, and leads 7.7%: 5.3% at 19% pot, 2.1% at 29% pot, 0.2% at 60% and 0.1% at 120%. Across the whole weighted flop set it checks 95.7%.

Now the cost question. Every one of these reports has a Simplify drawer that asks exactly what this article asks: force one action on every board, and see what it costs against the solver’s mix.

Read the caveat at the top of that drawer, because it applies to every number in this article: the loss is measured against an opponent who does not adapt. It is a floor, not the real price.

The pattern is the same as preflop, one level up. Picking a single size is nearly free if you pick one the solver uses a lot and expensive if you don’t:

• Blind vs blind, 50bb: always check costs under 0.01bb a flop, always bet 30% pot 0.01, always 14.4% pot 0.03, always 60% pot 0.06 — and always 120% pot 0.25bb.
• 100bb cash, big blind against an LJ open: always check is again under 0.01bb, always bet 25.5% pot costs 0.10, and always overbetting 200% pot costs 0.78bb a flop.

Notice which action is cheapest in both spots. Out of position, checking the whole range sits inside the solver’s own noise: the leads are worth so little that giving them up costs nothing measurable against a fixed opponent. They exist to make the other player’s life harder, which is exactly what a fixed-opponent measurement cannot see.

Where simplification really costs you

Everything above is measured against a solver opponent. That is the honest way to report it and it is also its limit. Three costs the numbers cannot show:

• Your opponent adapts. If you always check the flop out of position, a decent player bets more and folds less. The 0.00bb in the drawer becomes a real number as soon as anyone notices.
• The simplification travels. A range you always check has a different composition on the turn than a range you sometimes lead. The flop number does not carry the turn cost.
• You apply it too widely. This is the one the data does show, and it is the big one: 0.044bb a hand for one seat’s worth of wrong chart.

So, as a rule of thumb — my reading of the numbers above, not solver output:

• Collapse every mix you like. It is free within a spot, and a chart you can recall beats a chart you half-remember.
• Never reuse a chart across openers, stack depths or ante formats. That is where the measurable money goes.
• If you must keep one bet size, keep the one the solver plays most — and never the biggest one. In these two spots the biggest size costs 8 to 22 times what the smallest one does.
• Keep mixing where it is cheap to mix, if you can: the frequencies are what stop a thinking opponent from reading you.

Is simplifying the road to success? Simplifying how you remember the strategy: yes, and it is cheaper than almost anyone assumes. Simplifying how many situations you cover: that is not simplification, that is a leak with a friendly name.

Cheers! 🙂