Chip EV

Chip EV

5-max SnG, $50 buy-in. Payouts $120 / $60 / $30. Four players left: stacks A=2400, B=1800, C=1200, D=600 (your stack, 6 BB at the 100 blind level). UTG (big stack A) shoves. You hold AKo. Call or fold?

Pure chip EV: AKo against a big-stack shoving range (roughly 22%+, JJ+/AT+/22-77) runs about 52% equity. The pot before your call is 2400 (his shove) + 100 ante + blinds = ~2600 effective. Your call is 600. Chip EV of the call = +0.05 × 600 = +30 chips. Marginally plus.

Dollar EV with ICM: your bubble factor as the short stack against the big stack shove is ~0.6, meaning you need 38%+ equity to break even on the call — and you have 52%. In dollars the call is solidly +EV. This is an inverted example: the short stack on the bubble is actually making a profitable call in dollar terms, because ICM works in your favor here.

Flip the scenario. Same tournament, you're the middle stack at 1800 (B), big stack A shoves 2400. You hold TT. Chip EV: TT runs ~55% against his range, clean chip-EV profit. Dollar EV: bubble factor for the middle stack is ~2.5, requiring 71%+ equity to justify the call. You have 55%. Dollar EV is negative — fold is correct.

That is the core difference between chip EV and dollar EV: the chip math says one thing, the dollar math says another. Without understanding chip EV and its limits, you will systematically call –EV spots on the bubble and fold +EV spots against big stacks.

What It Actually Is

Chip EV is the expected value of a hand expressed in chips. Put 100 chips into a spot where you have 60% equity against a 200-chip pot: chip EV = 0.60 × 200 – 0.40 × 100 = +80 chips. Linear math, no consideration of what those chips are worth in prize-pool dollars.

In cash games this is the right framework. One chip at a cash table equals one unit of money. Wins and losses in chips convert directly to $. Maximizing chip EV equals maximizing dollar EV. Every classic concept, pot odds, implied odds, equity, operates in chip EV, and in cash games that model never breaks.

In tournaments, chip EV is only half the story. Tournament chips have nonlinear dollar value. A big stack's 1,000 chips are worth less in dollars than a short stack's 1,000 chips, because the short stack is closer to busting and those chips protect the minimum cash. That gap between chip EV and dollar EV is what we call ICM EV.

Understanding chip EV matters because it is the baseline model for every solver calculation. PioSolver, GTO+, and MonkerSolver all model game trees in chip EV. Their outputs are chip-EV-optimal strategies. To translate solver output into a tournament context you apply an ICM adjustment on top. You cannot use solvers correctly without understanding this distinction.

The Formula

The basic formula:

chip EV = equity × chips won – (1 – equity) × chips lost

Concrete example. You shove 1,500 chips into a pot of 300. Villain calls:

• Your equity: 50%
• Win: 1,500 chips (villain's stack) + 300 (pot) = 1,800
• Loss: 1,500 chips (your stack)

Chip EV of villain's call, holding 50% equity against you: chip EV = 0.5 × 1800 – 0.5 × 1500 = +150 chips

Villain with 50% equity profits +150 chips on average by calling. Positive chip EV, he should call.

For pot-odds calculations the formula shifts slightly:

required equity = call / (call + final pot)

Pot is 500, villain bets 200, you face a 200-chip call into a 700-chip pot. Required equity = 200 / 700 = 28.6%. Any equity above 28.6% makes the call chip-EV positive.

Use an equity calculator for precise equity against villain's range and a pot-odds calculator for the baseline math.

Chip EV vs Dollar EV (ICM)

This is the fundamental math divide in tournament poker. Commit it to memory.

Cash games always: chip EV = dollar EV. One table chip = one dollar. Every decision runs on pure chip EV math. ICM never applies to cash games.

MTT early stages (well away from the bubble): chip EV ≈ dollar EV. Divergence is minimal, all players are far from pay jumps. ICM adjustments shift decisions by 1–3%, which is usually below your equity estimation margin.

MTT middle stages: chip EV and dollar EV start diverging, especially with significant stack asymmetry. Sitting on 5 BB with 50 players left in a 200-player field, for instance: chip EV says shove wide, dollar EV (ICM) says shove even wider, a short stack's chips are nearly worthless anyway, so play pure cEV.

MTT money bubble: the gap becomes dramatic. Big stacks operate in "reverse math" (see Bubble factor). Decisions must be driven by ICM, not chip EV.

Final table bubble: divergence peaks. Bubble factor for middle stacks runs 2.5–3.5×. Pure chip-EV play here is catastrophic.

Satellites (winners receive identical seats): chip EV is nearly irrelevant. Win = seat, bust = 0, no prize gradient. ICM dominates completely.

Rule of thumb: use chip EV math when you are in a cash game, or when you are in a tournament well clear of any pay event, bubble, final table, major pay jump. Everywhere else, think in ICM.

Where Chip EV Works Perfectly

Cash games, always. The baseline decision model. Every cash-game situation runs through chip EV. Use solvers directly; no ICM adjustments needed.

Heads-up MTTs and SnGs. With two players remaining, ICM collapses toward chip EV, the winner takes everything, the loser gets the min-cash. Heads-up is the edge case where chip EV and dollar EV nearly converge. Solver strategies apply as-is.

MTT early stages (before 50% of the field is eliminated). The chip EV vs dollar EV gap here is under 5%, below equity-estimation noise. Just maximize chip EV.

Late stages with flat payout structures. Some tournaments (multi-seat satellites, for example) pay flat prizes, seats 1–9 each receive $100. ICM pressure is minimal on these stages and chip EV math holds.

Studying strategy with a solver. PioSolver and GTO+ model in chip EV. Study their output, understand what GTO balance looks like, then apply it directly in cash and with ICM adjustments in MTTs.

Where Chip EV Breaks Down

The money bubble. The $0 → $300 min-cash jump makes the short stack's chips worth more in dollars than chip EV suggests. Big stacks play tighter than chip EV prescribes (chips are nearly locked into the money). Middle stacks play tighter. Short stacks shove wider than pure chip EV recommends.

Final table bubble (9–10 players remaining). The largest pay jumps in the tournament. Bubble factor for middle stacks: 2.5–3.5×. A spot chip EV marks as +0.5 BB can carry –$300 in dollar EV in a major MTT.

Satellites. The "winner-takes-a-seat" structure breaks every chip-EV concept. A big stack must play extremely tight, chip EV labels those shoves as +EV, but in a satellite winning extra chips means nothing if you already effectively hold a seat.

Severe stack imbalances near major pay jumps. Say you are 20 players from the money in a 50-paid field sitting on 15 BB as a middle stack. Chip EV marks certain shoves as clear +EV. Dollar EV disagrees strongly.

Bounty tournaments (KO, Progressive KO). Here chip EV breaks in the opposite direction. The bounty value makes wide shoving correct because each elimination carries immediate dollar value on top of chip equity. Standard chip EV underestimates the profitability of aggression.

Push/Fold Preflop by Chip EV

With a short stack (10 BB or less), most decisions reduce to shove-or-fold. Nash equilibrium in chip EV produces unexploitable push/fold ranges. This is the foundational model for short-stack MTT strategy.

Concrete example: Nash shove range from UTG at 10 BB in 6-max:

• 22+, A2+ (all aces)
• K8s+, K9o+
• Q9s+, QTo+
• JTs, J9s
• T8s+, T9o

That is roughly 17.5% of hands. By the chip EV model this range shoves break-even against an optimal calling range from villain.

These calculations assume villain defends optimally. In practice, opponents overcall, loose calling ranges, which makes wide shoving even more profitable.

ICM adjustments generally narrow Nash shove ranges. On the bubble of a large MTT your chip-EV-correct shoving range typically tightens 30–50% because:

• Big stacks will not call you with marginal hands (they avoid flips on the bubble too)
• Middle stacks call tight (they have ICM pressure as well)
• Each elimination below the min-cash costs more in dollars than chip EV accounts for

Use an ICM trainer to adapt Nash push ranges for the ICM pressure of your current spot.

Preflop Calling Ranges by Chip EV

When villain shoves, your calling range is determined by his shoving range and the pot odds. The chip EV formula:

required equity = call / (call + dead money + shove)

Villain shoves 12 BB from UTG; you are on the BB with a 25 BB stack. Call is 12 BB into a 13.5 BB pot (1.5 BB blinds + ante + 12 BB shove). Required equity = 12 / 24.5 = 49.0%.

Against a Nash UTG shove range (~12%, JJ+/AK) your calling range needs 49%+ equity. That is TT+, AQ+, plus the occasional bluff-catcher (99) that squeezes out +0.5% chip EV.

In cash these calculations apply directly. On the bubble you need to tighten your calling range 30–50%. ICM adjustment pushes required equity up to 60–70%.

Post-Flop Chip EV

In post-flop play, chip EV drives optimal c-bet sizing, bluff-catching frequencies, and donk-bet decisions. All standard solver output is chip EV.

Concrete examples from solver literature:

C-bet sizing on ace-high flops: solvers recommend 33% sizing at high frequency (75%) and 100% sizing at lower frequency (25%). That recommendation is chip EV. In cash, apply directly.

Bluff-catching on the river with a medium pair: solvers recommend calling at minimum frequency (40%) against certain sizings. Works in cash. On the MTT bubble, folding more often is frequently correct because the dollar EV of calling is more negative due to Reverse Implied Odds.

BB donk-bet from the flop: GTO recommends donking on certain board textures (low connected boards). Chip EV recommendation. In MTTs this may need adjustment depending on proximity to pay jumps.

Solvers and Chip EV (GTO)

GTO (Game Theory Optimal) means maximizing chip EV against a theoretically optimal opponent. Tools like PioSolver, GTO+, and MonkerSolver model game trees to showdown and find Nash equilibrium strategies.

Every output from these solvers is in chip EV. Perfect for cash games. For tournaments you need:

ICM-aware solvers:

• HoldemResources Calculator (HRC) for push/fold spots
• ICMIZER 3 for late stages and final tables
• PioSolver with a custom ICM overlay for post-flop study in specific tournament spots

Without ICM, solver output is an approximation. Players often apply ICM adjustments by feel: "solver says shove 88 here by chip EV. I'll tighten 30% for the bubble," or "solver says call AT here. I'll tighten 50% for the final-table bubble." Intuitive, but imprecise. Pros use ICM-aware solvers directly for tournament decisions rather than eyeballing mental corrections.

Common Chip EV Mistakes

Applying chip EV math on the bubble. The most common error. A player learns pot odds in chip EV from cash-game study, then applies them on the final-table bubble of an MTT. Result: calling spots with –$50 in dollar EV instead of folding. Any time you are on a bubble or final table, verify the ICM adjustment.

Ignoring chip EV in cash games. The inverse mistake. A player studies ICM for tournaments and starts second-guessing every cash-game decision with "ICM thinking." ICM does not apply to cash. One chip = one dollar. Use chip EV directly, no adjustments.

Confusing chip EV and dollar EV in satellites. Satellites nearly break chip EV entirely. Evaluating satellite decisions through a chip EV lens produces systematic errors. Use only ICM-aware tools for satellites.

Over-applying ICM adjustment in the wrong spots. A player spooked by ICM plays tighter than necessary in early MTT stages. Result: arrives at the bubble already short-stacked. Early MTT stages call for chip EV maximization and aggressive shoving.

Transferring solver output directly to tournament play. A player takes PioSolver strategies (chip EV) straight to a final table. Without ICM adjustment those strategies are a direct path to elimination.

Ignoring variance when evaluating chip EV decisions. Maximizing chip EV is a long-run proposition. In a single hand you will often lose. Over thousands of hands, maximizing chip EV wins. Players tilt after making thin +EV calls by chip EV, not grasping that EV in one hand and EV over ten thousand hands are entirely different things.

Where This Framework Has Limits

Chip EV is an abstraction that simplifies calculation. It does not account for:

Variance. A thin +0.5 BB chip EV call has different practical value depending on whether you are a deep stack or a short stack. Middle stacks should often fold thin +EV spots to reduce variance.

Skill differential at the table. If a very weak player is at your table, your real tournament EV is higher than chip EV suggests. It can occasionally be correct to absorb a small chip EV loss to stay in action against a soft opponent.

Future streets at deep stack depths. Chip EV assumes current stack sizes. At 200 BB+, implied odds can shift the math substantially, and thin chip EV calls can become major long-run winners.

Additional use from deep stacks. Related to the above: deep stacks give you more ways to extract equity than standard chip EV calculations capture.

Chip EV is a baseline model, not a final answer. Use it as a starting point, then adjust for ICM, variance, opponent quality, and stack depth. A player who follows chip EV blindly plays at roughly 80–85% of optimal. A pro who understands chip EV and knows when to deviate plays at 95%+.