How Deep-Stack Poker Changes Implied Odds and Risk

In deep stack poker, the extra payoff needed barely changes with depth—about 18 bb without set over set, or 19.5 bb at 100 bb with it—but its share of the remaining stack and the risk do change. Under these assumptions, with a 3 bb open and pocket sixes, you need about 19.5 bb later at 100 bb—20.1% of the stack behind—after adjusting for set over set. At 200 bb, you need about 20.6 bb, or 10.5%. At 20 bb, it is impossible, while the cost of losing a full stack to a higher set grows with depth. The biggest sensitivity is the opening size: increasing it from 3 to 4 bb at 100 bb raises the required share from 20.1% to 27.1%.

This analyses one decision—calling with pocket sixes against one raiser, assuming the blinds fold—not the whole deep-stack strategy.

What counts as a deep stack?

A deep stack is large relative to the blinds, but sources use different thresholds. Here, you compare specific effective stacks rather than relying on the label.

• Upswing Poker, upswingpoker.com, in its article dated 22 August 2020, describes deep stacks in cash games as usually more than 100 bb, while its introduction uses 150 bb+ as a reference point.
• DeucesCracked, deucescracked.com, describes a format in its glossary where players typically start with 200 bb or more.
• PokerSkill, pokerskill.com, gives a set frequency of about once in eight and a half flops in its set-mining glossary. Its heuristic says that when a call costs more than roughly one-tenth of the effective stack, implied odds rarely cover it; at 50 bb or less, they usually do not cover the misses.

Upswing Poker also states that opening sizes remain the same as at 100 bb, while 3-bets become larger. Those decisions are outside this analysis.

Which decision are we calculating?

You are calculating how many extra chips your opponent must pay after the flop, on average, for your call with pocket sixes to break even.

The model assumes:

• You are playing no-limit Texas Hold’em cash.
• You are on the button with 66, facing one opponent’s open to 3 bb.
• The 0.5 bb and 1 bb blinds fold, leaving 1.5 bb of dead money.
• You call 3 bb; with an effective stack of S, you have S − 3 bb behind.
• If you miss a set on the flop, you lose your 3 bb call.
• If you hit a set and do not lose to a higher set, you receive the pot of 1.5 + 3 + 3, plus your opponent’s extra chips later.
• In a set-over-set loss, you lose the entire effective stack S.

The effective stack is the most you and your opponent can risk against each other. It is not necessarily your entire stack.

The probability of flopping a set is 11.755%, or 1 in 8.5: 1 − C(48,3) / C(50,3). The unknown is your opponent’s average payment after you hit. You are finding a minimum extra payoff for break-even, not predicting their behaviour.

How much do you need to win later?

Without accounting for set over set, you need to win 18.0 bb later, regardless of depth, provided the call still costs 3 bb.

For q = 0, where q is the probability of set over set conditional on you hitting:

Required extra payoff = call / set probability − dead money − 2 × call

3 / 0.11755 − 1.5 − 6 = 18.0 bb

The extra chips X are your opponent’s chips that you win later, excluding your own future bets. The pot odds and implied odds guide explains how they supplement the current pot odds.

Table A uses q = 0, with no set-over-set adjustment. Values are rounded to the precision shown.

“Reachable” means only that your opponent has enough chips. It does not establish that they will pay the required share.

How does depth change the share of the stack?

The more chips remain behind, the smaller the share represented by the required 18.0 bb in the q = 0 model. At 100 bb, it is 18.6%; at 200 bb, it is 9.1%. The teaching diagram below rounds those shares and excludes set over set.

Bars of the stack share needed to win for set-mining: 20 bb impossible, 40 bb 49%, 100 bb 19%, 200 bb 9%.Teaching diagram from our calculation: 3 bb open, pocket sixes, one opponent. It shows the share of the stack behind you that must be won (about 18 bb).

Stack depth and SPR are different measures. SPR (stack-to-pot ratio) is the remaining effective stack divided by the pot at the decision point; see SPR in the pot-committed guide for how it relates to decisions.

At 20 bb, calling leaves 17 bb behind—less than the required 18.0 bb even before rare large losses. The minimum stack in this simplified model is about 21.0 bb, or about 21.5 bb with the adjustment for the medium opening range.

PokerSkill’s heuristic points the same way for 20 bb: after calling 3 bb, you can win about 22 bb if your set takes all the chips, against a target of 30 bb. The source’s tenfold target refers to the full win, including dead money and your call. It is stricter than our 18 bb extra-payoff threshold: expressed as a full win per 3 bb called, our threshold is 7.5 = (18 + 1.5 + 3) / 3 times the call. That heuristic leaves a cushion for losses outside the model, so the two approaches do not contradict each other.

How can you repeat the calculation?

You can reproduce the baseline calculation without set over set in the pot odds calculator.

1. Enter 1.5 in “Pot size (before the bet)”.
2. Enter 3 in “Bet to call”.
3. Enter 11.76 in “Your equity”.
4. Enable “Add implied odds”.
5. Enter 18 in “Extra chips you expect to win if you hit”.

With the toggle enabled and a positive extra-chip value, the result reads: “To call now you need to win about 18 more chips later.” The required equity with implied odds is 11.8%, indicating a break-even call at the displayed precision. The probability input is rounded to 11.76%, and the displayed threshold to 11.8%.

Pot odds calculator with pot 1.5, bet 3, equity 11.76 and extra chips 18: a break-even call, win about 18 more chips later.Observation on the screenshot: with 18 extra chips the required equity with implied odds is 11.8%, a break-even call. The field prefix is “$”; in this example the units are bb.

Keep the two results separate: 18 bb is the calculator result at q = 0; 19.5 bb at 100 bb includes our set-over-set adjustment. The tool does not add that adjustment itself.

Which risk grows with the stack?

Depth increases the size of a rare full-stack loss and the spread of outcomes from one call. Set over set is the rarest of the risks considered: with the medium opening range, it occurs about once per 729 calls, but it is not the only way to lose chips.

Here, your opponent opens a medium range of 27% of hands: 358 combinations, including all pairs 77+. Conditional on you hitting, the set-over-set probability is 1.2%. Table B includes this risk; the standard deviation of one call is calculated at the break-even payoff.

Without set over set, the standard deviation of one call is 8.2 bb; including it at 300 bb raises that to 14.6 bb. Standard deviation measures the spread of outcomes, not the expected loss; see poker variance and downswings.

The set-over-set cost in EV—expected value—is 0.14 bb at 100 bb and 0.27 bb at 200 bb. A single such event, however, costs the entire effective stack. Poker bankroll management explains how the size of that loss relates to your available funds.

This is an example of reverse implied odds: making a strong hand can lead to a large loss rather than a payout.

Which assumptions change the result most?

The opening size has the largest effect in this comparison; the practical result also depends on the share your opponent pays on average. At 100 bb, increasing the open from 3 to 4 bb raises the required share from 20.1% to 27.1%.

Table C uses the medium range unless the row specifies otherwise.

The tight range contains 199 combinations and the wide range 597. Every range includes all pairs 77+. Changing the range changes the risk adjustment, but the table does not tell you how much your opponent will actually pay your set.

When does the model indicate a call or a fold?

Under these assumptions, facing a 3 bb open at 100 bb, the break-even threshold is about 19.5 bb of extra opponent chips, or 20.1% of the stack behind. If you expect an average payoff below the threshold, the model points to a fold; at or above the threshold, the call breaks even or has positive expected value only within the model.

At 200 bb, the required share falls to 10.5%, although the absolute amount rises to 20.6 bb. At 40 bb, you need 50.7%—roughly half the remaining stack. At 30 and 40 bb, the payoff is only theoretically reachable, not a reason to call automatically.

Estimate the average payoff after hitting, rather than the possibility of taking your opponent’s whole stack on one occasion.

What is not modelled?

The calculation does not cover every way to win or lose the hand. It isolates a call made to flop a set, with one risk adjustment.

• Rake and multiple opponents. No rake is deducted. Additional players change the pot, payoffs and risk of losing.
• Position and the blinds’ actions. Their folds are an assumption: after your button decision, both blinds can still act, including squeezing. If you are in the big blind, the dead money differs.
• 3-bets and a changing price to continue. The model does not calculate your response to a raise after your call.
• Turn and river sets. Only flop hits count. Excluding later sets pushes the threshold upward, making this part of the calculation conservative.
• The pair’s equity without a set. Showdown wins and bluffs are excluded: every missed flop costs 3 bb in the model.
• Your opponent’s draws. A set can lose to a flush or straight; those outcomes are not included in the set-over-set adjustment.
• Blockers from 66. They have not been removed from the ranges of 199, 358 and 597 combinations.
• The relationship between opening size and range. An opponent’s 4 bb opening range is narrower than their 2.5 bb range, but the opening-size comparison holds q constant.

The smaller required share at deeper stacks is therefore a property of this calculation, not a promise of profit. You still need to estimate whether your opponent will pay enough and how the excluded risks affect the decision.