Stack geometry: follow the chips from flop to river
A bet of 10 into 20 looks small beside a 70-chip stack. If it is called, though, the next pot is 40. Bet half of that and get called again, and the river pot is 80 with 40 left. The last half-pot bet is now an all-in.
That is the useful part of stack geometry. A percentage applies to a changing pot, so a sequence of modest-looking percentages can move an entire stack. This lesson follows both players’ chips, explains the equal geometric size, and gives you a planner for testing a different sequence. It answers an accounting question: what happens if these bets are called? It does not tell you whether those bets should be made.
Start with the pot-and-stack snapshot, use the interactive planner, or work through the exact 50% example. The rounding example explains why the final bet may differ from the displayed percentage.
Use the pot and stacks from the same moment
Take the snapshot at the start of a postflop betting round, before anyone has bet on that street. The pot contains chips already committed. Each remaining stack contains chips still in front of its owner. Do not put a player’s earlier contribution back into their stack, and do not subtract it from the pot.
For this heads-up model, the effective stack is the smaller of the two remaining stacks. If you have 70 and the opponent has 100, only 70 from each player can be matched. Their extra 30 is outside the modeled exchange. This remains true even if the bigger stack has enough chips to announce a larger wager; unmatched chips do not become additional money that the shorter stack can win.
Stack-to-pot ratio, or SPR, is effective remaining stack divided by the pot. Here it is 70 ÷ 20 = 3.5. Keep the moment attached to the number. An SPR before a bet and an SPR after its call describe different positions in the hand. The effective-stack drills give you more practice choosing the correct stack.
There is no side-pot calculation here. With three or more players, different pairs can have different effective stacks and different claims on the money. Taking the shortest stack at the table and using it as a single universal stack can erase those differences.
Set up a called path
The equal-size mode finds a theoretical pot percentage that uses the effective stack over the remaining streets. The displayed path then rounds bets to a chip increment and uses the exact remainder on the final street. Custom mode lets you request a separate percentage on each street; a request larger than the chips available is capped.
Use this away from a live hand, where your room’s software rules allow study tools. The calculator works locally in this page. It does not send these entries anywhere or save them. A folded hand, a raise or a different bet means you need a new snapshot.
Equal-geometric-bet planner
Start at the beginning of an unopened postflop street, with no bet to call. Exactly two players remain. Every modeled bet is called in full, with no raises, rake, fees or extra money. Amounts all use the same unit. A unit may be a chip, a dollar or a big blind.
The worked example below is available without JavaScript.
Why a called bet adds twice its size
Let P be the pot immediately before a bet, S the effective stack, and B the bet. One player moves B into the pot, and the other calls B. The next pot is P + 2B. Each player has spent B, so the next effective stack is S − B. Both changes matter.
If the bet is a fraction f of the pot, then B = fP. Substitute that into the pot update and you get Pnext = P(1 + 2f). A half-pot bet has f = 0.5, so the called pot doubles. A pot-sized bet has f = 1, so the called pot triples. A 25% bet makes it 1.5 times as large.
A common bookkeeping error is to update the pot to P + B. That counts the bet and forgets the call. Another is to remove 2B from one player’s stack. Each player pays one B. The pot receives both.
An exact three-street path at 50% pot
Start the flop with a pot of 20, your stack of 70 and the opponent’s stack of 100. Assume one bet and one full call on each street, with no rake. Half the pot is the same fraction each time, but the chip amounts are 10, 20 and 40.
| Street | Pot before | Bet + call | Pot after | Your stack / opponent |
|---|---|---|---|---|
| Start | 20 | None yet | 20 | 70 / 100 |
| Flop | 20 | 10 + 10 | 40 | 60 / 90 |
| Turn | 40 | 20 + 20 | 80 | 40 / 70 |
| River | 80 | 40 + 40 | 160 | 0 / 30 |
The effective SPR is 3.5 at the start, 60 ÷ 40 = 1.5 after the flop call, 40 ÷ 80 = 0.5 after the turn call, and zero after the river call. The opponent still has 30. Those chips did not enter the pot.
Check the ledger another way. The starting pot plus both stacks is 20 + 70 + 100 = 190. At the end it is 160 + 0 + 30 = 190. With no rake, new money or payouts during the sequence, this total cannot change. A mismatch usually means a missing call or a contribution counted twice.
The final pot of 160 is not a profit figure. It contains your own contributions, the opponent’s contributions and the 20 already in the middle. The planner does not know who wins, how often they win, or how much each player invested before the snapshot.
Derive the equal fraction
After n called bets of the same pot fraction f, the pot has been multiplied by 1 + 2f exactly n times. In symbols, Pfinal = P(1 + 2f)n. If each player contributes the full effective stack S, the same final pot is P + 2S.
Set those two descriptions equal, divide by P, and take the n-th root. The result is f = ((1 + 2S/P)1/n − 1) ÷ 2. Multiply f by 100 to express it as a percentage. P must be positive; n must be the number of remaining betting opportunities you actually model.
For the 20-and-70 example, 1 + 2S/P = 1 + 140/20 = 8. With three streets, the cube root of 8 is 2. So f = (2 − 1) ÷ 2 = 0.5, or 50%. This is exact, so whole-unit rounding does not disturb that path.
You can also start with a percentage and ask how much stack the sequence can use. Rearranging gives S = P[(1 + 2f)n − 1] ÷ 2. Three called half-pot bets use 3.5 times the starting pot. Two use 1.5 times the starting pot. One uses half the starting pot. These are accounting identities under the stated assumptions, not hand-strength thresholds.
One less street changes the answer
Suppose the flop checks through with the same pot of 20 and the same effective stack of 70. Only turn and river remain. The equal fraction is now (√8 − 1) ÷ 2, approximately 91.421356% of the pot. With hundredth-unit chips, the rounded turn bet is 18.28, the call makes the pot 56.56, and the exact river remainder is 51.72.
If the turn also checks through, the river is the only betting opportunity left. Putting all 70 into a pot of 20 is a 350% pot bet. This does not mean checking earlier was a mistake. It tells you what the chosen final-stack target would require after those checks. The appropriate target may have changed with the action or board.
The two-street preset gives a cleaner overbet example. With 12 in the pot and 90 effective, SPR is 7.5. Then 1 + 2 × 7.5 = 16, its square root is 4, and the equal size is 150%. Bet 18 into 12 and get called: pot 48, stack 72. Bet 72 into 48 and get called: pot 192, stack zero. Each bet is exactly one and a half pots.
Those above-pot opening bets require a structure that permits them. The model assumes no-limit-style sizing and still does not check every legal constraint. In pot-limit, an unopened bet cannot exceed the pot. This page deliberately leaves raise-to amounts, prior wagers and reopening action to their own rules lessons.
A different sequence can reach the same final pot
Try the custom preset with pot 20, effective stack 70, and requests of 25%, 50% and 100%. The flop bet is 5, so the called pot is 30 and 65 remain. The turn bet is 15, so the called pot is 60 and 50 remain. The requested river pot bet would be 60, but only 50 can be matched. The planner caps that final bet at 50.
The actual river size is 50 ÷ 60 = 5/6 of the pot, or 83⅓%. The final pot is still 160. Both this path and the 50% / 50% / 50% path contribute 70 per player. Their intermediate pots and remaining stacks differ. That difference matters when you review the choices available on the turn and river.
Now enter 25%, 25% and 25% with a 0.01-unit increment. The bets are 5, 7.50 and 11.25; the pot finishes at 67.50, and 46.25 of the 70 effective stack remains. Custom mode reports the result you asked for. It does not quietly shove the remainder to imitate equal-size mode.
Rounding changes the actual percentages
A theoretical size can require a fraction of a chip. Start with pot 10 and 21 effective over three streets. The equal fraction is approximately 36.6239105%. With whole-unit chips, the first ideal bet is about 3.6624, which rounds to 4. The called pot is then 18. Applying the same unrounded fraction gives about 6.5923, which rounds to 7. The pot is now 32 with 10 left.
The final bet is the remaining 10, which is 31.25% of the 32 pot. The actual percentages are 40%, about 38.8889%, and 31.25%. Calling all three bets “36.62%” would hide what the chips actually did.
| Chip increment | Flop bet | Turn bet | River remainder | Final pot |
|---|---|---|---|---|
| 1 | 4 | 7 | 10 | 52 |
| 0.01 | 3.66 | 6.34 | 11 | 52 |
With 0.01-unit chips, the first called pot is 17.32 and the second is 30. The last 11 is approximately 36.6667% of that pot. Finer increments get closer to the theoretical sequence, but the final amount still follows the remaining stack. Both paths contribute exactly 21 per player.
The planner rounds non-final geometric bets to the nearest selected increment, with an exact half increment rounded up. It then caps a bet at the effective stack. The final street commits the exact remainder. The initial pot and both stacks must already be whole multiples of that increment; the calculator rejects incompatible entries rather than altering your starting snapshot.
A tiny stack exposes the limit of the ideal curve. With pot 10, stack 1, three streets and whole-unit chips, the ideal fraction is about 3.132928%. Both early bets round to zero; the last street uses the one chip. The tool labels those early steps as checks. That is a rounded accounting path, not three legal positive bets. Minimum opening bets and short-all-in rules still belong to the game you are reviewing.
Know when this path has stopped describing the hand
The calculation is conditional on calls. If the opponent folds on the flop, the turn and river rows never happen. If the opponent raises, the next pot and remaining stack come from that raise and your response, not from this path. Re-enter the actual state at a later unopened street if you want a new projection.
If you are already facing a bet, do not enter a pot that includes it and treat the resulting first row as an opening bet. This planner has no amount-to-call input and no raise model. Finish reconstructing the current action first. A later street, with all completed contributions in the pot and updated stacks behind, gives you a clean starting point.
Rake is excluded. If a game removes chips while the hand develops, the next pot may be smaller than P + 2B. If rake is taken only when the pot is awarded, the displayed betting path can still describe the gross pot, but it does not give the winner’s payout. Bonuses, bounties, multiple boards, side pots and tournament prize effects are also outside this model.
There is no hand, range, board or response model in these inputs. Two hands with identical pot and stack numbers may call for very different decisions. Equal geometric sizing does not prove that a bluff works, that a value bet gets called, or that a hand should play for stacks. For the decision itself, start with a stated goal for the bet.
Check your understanding without the calculator
Pot 16, stack 56, three streets: what are the equal-size bets?
The starting SPR is 56 ÷ 16 = 3.5, the same as the 20-and-70 example. The equal fraction is 50%. The bets are 8, 16 and 32. The called pots are 32, 64 and 128; the remaining effective stacks are 48, 32 and zero. Scaling the pot and stack by the same factor preserves the fraction.
Pot 30, both players have 45, and two streets remain. Does half-pot fit?
Yes. Bet 15 into 30 and get called: pot 60, each stack 30. Bet 30 into 60 and get called: pot 120, each stack zero. Two called half-pot bets use 1.5 times the starting pot, exactly 45 here.
The pot is 40, you have 25 and the opponent has 200. What is the effective stack?
It is 25, so starting SPR is 25 ÷ 40 = 0.625. If each player contributes all 25 effective chips, the final gross pot is 90 and the opponent has 175 left. Using 200 as the effective stack would invent chips you cannot match.
Pot 20, stack 70: what happens after 0%, 50% and 50%?
The first street checks through. A 10 bet and call make the pot 40, leaving 60 effective. A 20 bet and call make the pot 80, leaving 40 effective. A check consumes a street without growing the pot. Custom mode does not force those last 40 chips into the middle.
Keep the snapshot with your hand notes
Write down the street, pot, both remaining stacks, chip increment, proposed bets and assumed responses. Then record where the actual hand departed from that path. This makes a later review much more useful than a bare note saying “wanted to get all-in by the river.”
Use the poker study routine to keep a few worked hands together, or return to Info & tools for the related accounting lessons.