Expected Value in Poker Tournaments

Cash games:

• Every chip = its dollar value (USD 1 chip = USD 1).
• Maximising +EV decisions = maximising winnings.
• Standard EV calculation: EV = (win amount × win probability) - (loss amount × loss probability).

Tournament games:

• Chips don't have linear monetary value.
• Last 10% of chips you can possibly have are worth far less than first 10%.
• Why: tournament payouts are stepped (e.g. 1st = 30%, 2nd = 18%, 3rd = 12%, ...).
• Once you have 'enough chips to make the money', additional chips have diminishing returns until you cross next pay jump.

Implication:

• You can play a +chip-EV hand that's -dollar-EV due to ICM.
• This is the central insight tournament players need to internalise.

What ICM does:

• Calculates each player's expected share of the prize pool based on current stack distribution.
• Assumes no skill edge going forward (each player has equal probability of doubling up if all-in 50/50).
• Provides 'cash value' of your current chip stack.

Worked example - bubble scenario:

• Tournament: 50-player MTT, GBP 100 buy-in, top 10 paid.
• 11 players remain. Pay jumps: 11th = nothing, 10th = GBP 200, ... 1st = GBP 2,000.
• You have 50 BB (big blinds). Average stack = 40 BB. Short stack = 15 BB.
• ICM gives you ~GBP 460 cash value of current stack.

Doubling up vs busting at the bubble:

• Doubling: your stack now 100 BB; ICM cash value ~GBP 750 (gain GBP 290).
• Busting: you go from GBP 460 to GBP 0 (loss GBP 460).
• Net: a 50/50 call to double = GBP -85 EV in actual money (loss > gain × probability).
• Despite being +chip-EV, it's significantly -dollar-EV.

Phase 1 - Early stages (well above money):

• Tournament is large; pay jumps far away.
• Chip EV ≈ Dollar EV.
• Play +chip-EV poker without ICM concerns.
• Skill edge matters more than ICM here.

Phase 2 - Money bubble + early money:

• ICM most aggressive.
• +chip-EV calls can be significantly -dollar-EV.
• Tighten ranges; avoid all-ins unless dominant.
• Look for spots to fold what cash-game player would call.

Phase 3 - Pay jumps + final table:

• ICM still strong but less than bubble.
• Mid-stack should be careful; large stack can pressure.
• Final-table pay jumps (10th to 9th, etc.) create ICM moments.

Phase 4 - Heads-up:

• Two players left; winner takes most.
• Returns toward chip-EV thinking.
• Still slight ICM effect (chops via deals are negotiated).

Small stack at the bubble:

• Has least to lose (almost certainly busting if ICM-folded).
• Best play: ship it on any reasonable hand; force decisions on others.
• Others should call with WIDER range than ICM suggests because the short stack is shoving so wide.

Medium stack at the bubble:

• Highest ICM risk: stack has cash value to lose, no incentive to bust.
• Best play: TIGHTEN range substantially; let short stack bust first.
• Avoid spots where small mistakes compound into bubble bust.

Big stack at the bubble:

• Most freedom; can pressure medium stacks.
• Best play: aggressive against medium stacks; carefully against short stacks.
• Force ICM pressure on others.

Practical bubble pattern:

• Short stack shoves wide (no choice).
• Medium stacks fold (preserve stack).
• Big stack pressures medium stacks.
• Eventually short stack busts OR medium stack makes ICM mistake.

Cash game (no ICM):

• To call a pot-sized all-in: need ~33% equity (you're getting 2:1 on call).
• Below 33% = -EV; above 33% = +EV. Simple.

Bubble situation (max ICM):

• To call an all-in vs short stack at bubble (taking 1:1 on call): may need 50-55% equity.
• The 5-10% extra equity required reflects ICM.
• Means many cash-game +EV calls are -EV in tournament.

Pay-jump situation (moderate ICM):

• Need ~40-45% equity for many calls.
• ICM impact smaller but still meaningful.

Approximation rules:

• Cash game call requires ~33% equity → Bubble call needs ~50%.
• Cash game call requires ~50% equity → Bubble call needs ~60%.
• Cash game call requires ~60% equity → Bubble call needs ~67%.

ICMIZER:

• Most popular offline ICM analysis tool.
• Run hand histories through; see optimal vs your decisions.
• Reveals systematic ICM mistakes.
• ~USD 30/month.

HoldemResources Calculator:

• Specialised for push/fold ICM calculations.
• Pre-computed charts for common spots.
• ~USD 50/month.

Equilab:

• General hand-equity tool + ICM module.
• Free version available with limited ICM features.

In-game intuition:

• Tighten ranges by 5-15% at the bubble.
• Avoid coin-flips with medium stack against medium stack.
• Force small stack to make moves.
• Develop through repeated study + reflection.

1. Skill edge ignored: ICM assumes no skill edge going forward. Aggressive players actually have +cEV beyond ICM. Adjust ranges based on remaining player skill.
2. Future game flow ignored: ICM doesn't account for upcoming hands' position, stack changes, blind levels.
3. Risk preferences ignored: ICM assumes profit-maximising play. Some players legitimately have lower risk tolerance (semi-pros) and may want even more conservative play than ICM suggests.
4. Deals + chops change calculations: if players agree to a deal at bubble/final table, post-deal play is closer to cash-game EV.
5. Reentries / rebuys change dynamics: ICM calculations need adjusting for buy-in tournaments where rebuy is available.