Chapter 6: Math

Pot Odds: The Equity You Need to Call

Formula: bet ÷ (pot + bet × 2)

Bet size	Equity needed	Win 1 in 3 is enough (est.)
25%	16.7%	1 in 6 is enough
33%	19.9%	1 in 5
50%	25.0%	1 in 4
66%	28.4%	1 in 3.5
75%	30.0%	1 in 3.3
100%	33.3%	1 in 3
150%	37.5%	1 in 2.7
200%	40.0%	1 in 2.5

MemorizeMemorize this. There is no time to calculate during play. Remembering just these eight numbers is enough.

Check with the calculator (Pot odds)

MDF: The Lower Limit So You Do Not Fold Too Much

Formula: pot ÷ (pot + bet)

Bet size	Minimum frequency to defend	Most you can fold
25%	80.0%	20.0%
33%	75.2%	24.8%
50%	66.7%	33.3%
66%	60.2%	39.8%
75%	57.1%	42.9%
100%	50.0%	50.0%
150%	40.0%	60.0%
200%	33.3%	66.7%

The smaller your opponent bets, the less you may fold (against a 33% bet, defend 75.2%). But MDF is “the lower limit so you are not exploited”; against an opponent who does not bluff, you do not need to defend it.

Check with the calculator (MDF)

The Ratio of Value to Bluffs

The calculation for the side that bets on the river. The formula is the same as pot odds

Bet size	Share of bluffs	Value : bluff
33%	19.9%	4 : 1
50%	25.0%	3 : 1
75%	30.0%	2.3 : 1
100%	33.3%	2 : 1
150%	37.5%	1.7 : 1
200%	40.0%	1.5 : 1

What it means

• The bigger you bet, the more bluffs you can add = because you are asking your opponent for more folds
• Put the other way, if you bet big, first check that you have enough bluffs
• Betting big without enough bluffs leans you toward value, and you get read and folded against

Estimating Equity: The Rule of 2 and 4

Outs × 2 = the probability of completing with one more card, outs × 4 = with two cards

Draw	Outs	By the turn	By the river
Flush draw	9	19.1%	35.0%
Open-ended straight draw	8	17.0%	31.5%
Gutshot	4	8.5%	16.5%
FD + OESD	15	31.9%	54.1%
Two overcards	6	12.8%	24.1%
Pocket pair → set	2	4.3%	8.4%

Note: you can use × 4 only when you will actually see both of the two cards (such as when all-in). If you will face another bet on the turn, calculate with × 2. Mix this up, and the basis for your call falls apart.

Check with the calculator (Outs)

Implied Odds and Reverse Implied Odds

Why you can or cannot call even when the current odds are not enough

Implied odds

• Calculate including what you can win in addition when you complete
• Conditions: deep stacks, an opponent who pays, a hidden hand
• This is the basis for sets and suited connectors

When it does not hold

• The stacks are shallow (low SPR)
• The opponent is tight
• The completion is easy to see (four to a flush)

Reverse implied odds

• Calculate including the chance of losing even more after you complete
• It arises when you are dominated
• The basis for not calling with A9o and KJo

How to tell them apart

• “When I hit, what hands will my opponent pay with?”
• If every hand that pays is better than yours, those are reverse odds

Even with the same 20% draw, it has value if you can win big when you hit, and no value if you lose even when you hit. This is the part that pot odds alone cannot decide.

Combo Counting: How Many the Board Removes

The work of turning your opponent’s range into numbers

Hand shape	Base	One on the board	Two on the board
Pocket pair (AA)	6	3	1
Unpaired (AK)	16	12	9
Suited only (AKs)	4	3	2
Offsuit only	12	9	7
When you hold one card yourself	－	The same calculation as above	－

How to use it in real play

• Name three kinds of value hands for your opponent and add up the combos (example: AK 9 + AA 3 + KK 3 = 15, before counting your own hand)
• Count the bluff candidates the same way
• See whether bluffs ÷ total exceeds the equity needed from pot odds

EV Calculation: When a Bluff Works

Formula: success rate × pot − (1 − success rate) × bet

Example: a 7BB bluff into a 10BB pot

Assuming your opponent folds 45% of the time

0.45 × 10 = +4.5BB

0.55 × 7 = −3.85BB

Total = +0.65BB

So this bluff makes a profit.

Whether to bluff is not a matter of taste; this one line decides it.

The break-even point

• Success rate needed = bet ÷ (pot + bet)
• 7 ÷ 17 = 41.2%
• If they fold 41.2% or more, the bluff works

Points to watch

• “The chance they fold” is an estimate. It is the only uncertain element
• That is why observing your opponent decides how accurate this formula is
• Even if the formula is correct, rough inputs give a rough answer

Check with the calculator (Bluff EV)

These Are the Only Numbers You Really Use in Play

The rest is enough if you can calculate it during review

Pot odds, 4 numbers	25%→16.7% / 33%→19.9% / 50%→25.0% / 100%→33.3%
MDF, 3 numbers	33% bet→75.2% / 50%→66.7% / 100%→50.0%
Draws, 3 numbers	FD 35.0% / OESD 31.5% / gutshot 16.5% (by the river)
Ratios, 2 numbers	50% bet→bluffs 25.0% / 100%→33.3%
Combos, 3 numbers	Pair 6 / unpaired 16 / suited 4

Remembering just these 15 numbers makes calculation during play almost unnecessary. MemorizeMemorize this.