What Is Geometric Bet Sizing? Calculation & When to Use It
Learn geometric bet sizing in poker — why betting the same pot fraction each street is optimal, how to calculate it from SPR, and when to use it at the table.
📝 Where this fits: Advanced — assumes familiarity with bet sizing basics. This article also uses concepts like MDF (Minimum Defense Frequency), SPR, and polarized ranges. For SPR fundamentals, see Understanding Stacks, Effective Stacks & SPR.
What Is Geometric Bet Sizing?
"I want to get all-in by the river — but how much should I bet on each street?" The theoretical answer to this question is geometric bet sizing.
Geometric bet sizing means betting the same fraction of the pot on every remaining street so that your last bet is exactly all-in. It is also known as GGOP (Geometric Growth of the Pot).
For example, with SPR 3 and two streets remaining, betting about 82% of the pot on each street gets you exactly all-in. That is a geometric bet size.
The key point is "same fraction of the pot," not "same dollar amount." Because the pot grows after each bet and call, the actual dollar amount increases on later streets.
Why Is the Same Fraction Optimal?
To understand why geometric bet sizing is optimal, let's walk through a thought experiment.
All-In vs. Spreading Bets Across 3 Streets
The GTO Wizard blog presents the following thought experiment.
Imagine a flop with a 1,300 in stacks (SPR 13). You hold the nuts and want to get your entire stack into the pot by the river.
Strategy A: Shove all-in on the flop ($1,300)
Following MDF, your opponent can only call with 1 ÷ (1 + 13) ≈ 7% of their range. On average, they put 91** into the pot.
Strategy B: Spread bets across 3 streets (equal fractions)
Betting 100% of the pot on each street gets you exactly all-in over 3 streets. Your opponent must defend at MDF = 1 ÷ (1 + 1) = 50% on each street, so the probability of calling all three streets is 50% × 50% × 50% = 12.5%.
But opponents who fold along the way have already paid into the pot up to that point. Overall, the average amount your opponent contributes is about $237 — 2.6 times more than Strategy A.
Key takeaway: When you want to get all the chips in, spreading bets across multiple streets extracts more from your opponent than a single all-in. And the more uniform the bet sizes across streets (= geometric), the more your opponent's total calling frequency is maximized.
From an MDF Perspective
Why does a uniform fraction force the widest calling?
Your opponent defends at MDF on each street to avoid being exploited by bluffs. The probability of calling all streets is the product of each street's MDF.
This product is maximized when each street's MDF is equal — that is, when the bet size (as a pot fraction) is equal on each street.
For example, even when deploying the same total stack, betting small on the flop and making a huge overbet on the river causes the river MDF to shrink dramatically. The overall call rate drops. Betting large on the flop and small on the river does the same thing. The greater the variance in bet sizes, the lighter your opponent's calling obligation becomes.
Also Beneficial for Bluffs
"If the opponent calls more often, shouldn't I avoid bluffing?" you might think. It's actually the opposite.
Geometric sizing forces the widest defense from your opponent. Conversely, deviating from geometric sizing lightens their calling obligation, meaning they need to call less to defend against bluffs.
In a polarized strategy, you bet value hands and bluffs together. Because geometric sizing forces the widest defense, both the value extracted and the number of bluff combos you can include in your betting range are maximized.
How to Calculate It
For 2 Streets
Let S be the SPR. The geometric bet size r solves the following quadratic equation:
r + r(1 + 2r) = S
Solving:
r = (−1 + √(1 + 2S)) ÷ 2
For 3 Streets
Similarly, betting the same pot fraction r on all 3 streets to go all-in yields a cubic equation. The exact calculation is more involved, but the reference table below is sufficient for practical use.
Geometric Size by SPR
| SPR | 2 Streets | 3 Streets |
|---|---|---|
| 1 | 37% | – |
| 1.5 | 50% | – |
| 2 | 62% | – |
| 3 | 82% | 46% |
| 4 | 100% (pot-size) | 54% |
| 5 | 116% (overbet) | 61% |
| 6 | 130% | 68% |
| 8 | 156% | 79% |
| 10 | 179% | 88% |
| 13 | – | 100% (pot-size) |
💡 Mental math shortcut (2 streets): Add 1 to the SPR and divide by 5. For example, SPR 3 → (3+1)÷5 = 0.8 → 80% (exact value is 82%). Accurate within 5% for SPRs from 1.5 to 5.
For a mathematical derivation and accuracy analysis of this approximation, see the column below.
Worked Example: 100BB Cash 3-Bet Pot
BTN opens to 2.5BB, BB 3-bets to 10BB, BTN calls. The flop pot is about 20BB with effective stacks around 90BB.
- SPR ≈ 4.5: The 3-street geometric size is about 58%
- After a 33% c-bet is called → turn pot is about 33BB, stacks about 83BB, SPR ≈ 2.5 → the 2-street geometric size is about 72%
In 3-bet pots the SPR is low enough that geometric sizes fall within normal betting ranges, making them practical to apply.
When to Use It
Geometric bet sizing works when three conditions are met.
1. You Have a Nut Advantage
Your range contains more premium hands (sets, straights, flushes, etc.) than your opponent's. Geometric sizing is part of a polarized strategy, so it requires nutted hands in your range.
2. The Board Is Static
A board where equity is unlikely to shift significantly on later streets. For example, a rainbow dry board like K♠7♦3♣ barely changes the hand strength hierarchy regardless of the turn card.
Geometric sizing relies on the assumption that "the nuts stay the nuts." On dynamic boards (many draws, etc.), this assumption breaks down.
3. Your Range Is Polarized
Your range consists of nutted value hands + bluffs, with few medium-strength hands.
Hypergeometric Sizing
Sometimes it's correct to bet even larger than geometric. This is called hypergeometric sizing.
The main purpose is equity denial. When your opponent holds flush draws or straight draws, betting larger than geometric:
- Denies your opponent correct odds to continue
- Gets all-in before the river, eliminating uncertainty on later streets
- Drastically reduces implied odds
Hypergeometric sizing focuses on forcing folds to deny equity, rather than maximizing how wide your opponent calls.
For a detailed theoretical analysis of this concept, see the column below.
Summary
🎯 Key Points
- Definition — Bet the same pot fraction on each street so that your final bet is exactly all-in
- Why it's optimal — Forces the widest defense from your opponent, maximizing both value extraction and bluff construction
- Mental math — For 2 streets: (SPR + 1) ÷ 5 gives a quick approximation
- When to use — Nut advantage + static board + polarized range
- Beyond geometric — Against draws, hypergeometric sizing (larger bets) can be the better choice
For a deeper dive into the math behind geometric sizing or the theory behind hypergeometric bets, check out the related columns above.
Related Articles
Review bet sizing fundamentals:
Found this helpful?
Bookmark this page to revisit anytime!
Ctrl+D (Mac: ⌘+D)
Found an error or have a question about this article? Let us know.
✉️ Contact Us
