Interactive poker math reference

Master the Math
of Poker

Pot odds, equity, variance, MDF — every calculation a winning player runs, now interactive and visual.

♠ ♥ ♦ ♣
01 — Fundamental

Pot Odds

Minimum equity needed to make calling profitable.

eq_needed = call ÷ (call + pot)
Pot Size$100
Bet to Call$75
Your Estimated Equity40%
Call
Pot
Equity Needed
Your Equity
Pot Odds Ratio
Call EV
Mental shortcut: Pot-sized bet → need 33% equity. Half-pot → 25%. 2× pot → 40%. Villain bets 75% pot? You need ~43%.
02 — Game Theory

Alpha & MDF

Bluff break-even frequency & the minimum you must defend.

α = bet ÷ (bet + pot)
MDF = 1 − α = pot ÷ (pot + bet)
GTO bluffs/value = α ÷ (1−α)
Pot Size$100
Bet Size$75
ALPHA — fold needed 42.9% MDF — must defend 57.1% 0% 100% 0% 100% α + MDF = 100% | bet-to-pot: 75% | bluffs/value: 0.75
Alpha (α)
MDF
Bet / Pot
Bluffs per Value
Reading this: If you bet $75 into $100, villain needs to defend 57% of their range. If they fold more than 43%, every bluff is instantly profitable — even 7-2 offsuit.
03 — Call Analysis

Equity Required to Call

Visual breakdown of how each bet size changes the equity threshold.

eq = call ÷ (call + pot)
EV = equity × pot − (1−equity) × call
Pot Size$100
Bet to Call$50
66.7% WIN RATE Your equity needed 33.3% Villain's fold equity 66.7%
Equity Needed
New Pot if Call
Return on Risk
EV (at break-even)
$0.00
The pie shows the split: your slice (equity needed) must be at least this large for the call to break even. Bigger bets shrink the pot odds — you need more equity.
04 — Mental Math

Rule of 2 & 4

Estimate equity from outs instantly at the table.

Flop (2 streets): outs × 4%
Turn (1 street): outs × 2%
Exact flop: 1 − (47−n)/47 × (46−n)/46
Outs9 outs
Rule ×4
36%
36.0%
Exact
35%
34.97%
Outs
9
Rule Estimate
Exact Equity
Error
The rule overestimates slightly because it ignores card removal. At 9 outs on the flop the error is under 1.1%. For 15+ outs the rule can overshoot by 3–5% — adjust mentally.
05 — Statistics

Variance & Bankroll

How wide your results can swing — and how big a bankroll survives it.

SE = σ / √(N/100)
95% CI: WR·N/100 ± 1.96·σ·√(N/100)
BR = σ² / (2·WR) · ln(1/RoR)
Expected Win
95% CI Low
95% CI High
Bankroll (BB)
Adjust the inputs above to model your situation.
06 — Advanced

Implied Odds

Future winnings can justify calls that look wrong on pot odds alone.

pot_odds_eq = call ÷ (call + pot)
implied_eq = call ÷ (call + pot + future)
EV = equity × (pot + future) − (1−eq) × call
Current Pot$100
Bet to Call$50
Expected Future Winnings (when you hit)$150
Your Equity20%
Pot odds need
Implied need
Your equity
Pot Odds Need
Implied Need
Your Equity
EV of Call
Caveat: Implied odds are only real with disguised hands (sets, straights, flushes). Flush draw implied odds are lower — villain sees the board and may not pay off. Position amplifies implied odds dramatically.
07 — Stack Dynamics

Stack-to-Pot Ratio

SPR tells you what hand strength is required to commit on the flop.

SPR = eff_stack ÷ pot
Effective Stack (smaller of two)$200
Pot Size at Decision$50
Low (<4) Medium (4–13) High (>13) 4.0
SPR
Zone
Commit With
Streets to Stack Off
SPR 0–4
♠ Low SPR
Stack it off with any pair or strong combo draw. Fold equity is minimal.
SPR 4–13
♦ Medium SPR
Need top pair good kicker or better. Sets and two pair are golden.
SPR 13+
♣ High SPR
Need the nuts or near-nuts. Top pair becomes a bluff-catcher.
SPR + bet sizing: Pot-sized bets on each street triple the pot per street. With SPR 9, you commit with 3 pot-sized bets. With SPR 3, the money goes in on the flop alone.
08 — SPR in Context

Commitment: Full Picture

Board texture, position, and field size all shift how much equity you need before committing.

base threshold = SPR ÷ (1 + 2×SPR)
adjusted by texture · position · players
SPR4.0
Estimated equity when called / all-in55%
Board Texture
Your Position
Players in Pot
Adjustments: Base: — Board: — Position: — Players: — Threshold: —
20%30%40%50%60%70%80%+
Base Threshold
Adjusted Threshold
Your Stack-off Eq
Edge
Board Texture
Position
Field Size
Stack-off Equity
10 — Mental Math

Table Math Shortcuts

Fast arithmetic tricks for calculations you need without a calculator.

Trick 1
Distributive Split
Round A to the nearest 10, multiply, then add or subtract the leftover chunk.
×
Trick 2
Round & Compensate
When A is close to a round number, overshoot it, multiply cleanly, then subtract the overage.
×
Trick 3
Halve & Double
Repeatedly halve the even number while doubling the other. Each step is the same product — stop when one factor is easy to multiply. Best when A is a power of 2 or has many factors of 2.
×
Poker use: Figuring out 16 big blinds × 3.5 (3.5bb open) = 8 × 7 = 56bb total. Or stack-to-pot conversions with awkward stack sizes.
More Tricks
Trick 4
Multiply Any 2-digit by 11
Place the two digits at either end — their sum goes in the middle. Carry if the sum exceeds 9.
Trick 5
Near-100 Deficit Method
Find each number's distance from 100. Cross-subtract for the left digits; multiply the deficits for the right.
×
Trick 6
Difference of Squares
When A and B are equidistant from a round midpoint M, use M²−d². Works for 23×17, 28×32, 45×55.
×
Trick 7
Square Any Number Ending in 5
Take the tens digit n, compute n×(n+1), then append 25. Instant squares: 35²=1225, 75²=5625, 115²=13225.
More Tricks
Tool
Divisibility Checker
Enter any number — see which divisors apply and the rule behind each check.
Trick
Chunking
Break the dividend into easy multiples of the divisor, divide each chunk, sum the results. No long division needed.
÷
Poker use: Splitting a $756 pot 6 ways, or converting an odd stack size into BBs.