# Mathematical formula collection.

• Bronze
Joined: 24.05.2008
I see questions quite often for the quite simple formulas so i thought i'd gather them in one post. Hopefully some of you can have some use for it. Also posted some examples for them to see how they are used. If there is something missing or any misstakes, please let me know.

Mathematic formulary for poker.

Odds:
(unknown cards - outs) : outs

Pot odds:
(Pot+Bet):Investment

Implied odds
Draw odds - pot odds = implied odds needed

Equity to call bet:
EQ=Bet/(Pot+2*Bet)

Pot odds <=> Equity
x:1 => 1/(x+1)=EQ
1/EQ-1=x => x:1

EV-Calculations
( EV= P(1)*\$(P(1))+ P(2)*\$(P(2))+…+ P(N)*\$(P(N)) )

Calling a bet:
EV= P_win*(Pot+Bet) - P_lose*Bet

Fold equity:
EV= P_fold*Pot + (1 – P_fold) * (EQ * Total pot – Investment)

Purebluff FE, EQ=0:
EV= P_fold*Pot - (1 - P_fold)*Investment

Tournament maths
M-factor
M=Stacksize/(bb+sb+Ante*Players) *

Effective M-factor
EM = M * (players/10)

Effective Big Blind
EBB=2*(bb+sb+Ante*Players)/3 *

*A little trick is to replace (bb+sb+Ante*Players) with (Pot before any action preflop) for calculations on the table.
• 3 replies
• Bronze
Joined: 24.05.2008
Examples

Odds:
Flush draw from flop to turn gives 9 outs. 52-5= 47 unknown cards.
47-9:9
38:9
4.2:1

Pot odds:
To call a bet of \$8 into a \$10 pot.
(10+8):8
18:8
18/8:8/8
2.25:1

Implied odds:
To call a bet of \$5 into a \$5 pot with a flush draw on the flop.
Pot odds (5+5):5 => 2:1
Odds with flush draw 4.2:1
4.2:1 – 2.2:1 = 2.2:1
\$5*2.2 = \$11 needed to break even on later streets.

Equity to call bet:
To call a 10\$ bet in a 15\$ pot.
EQ=10/(15+2*10)
EQ=0.286 => 28.6%

Pot odds <=> Equity
Pot odds of 3:1 gives:
1/(3+1)=0.25 => 25%
Equity of 40% gives (EQ=0.4):
1/0.4-1=x
2.5-1=1.5
Pot odds 1.5:1

EV-Calculations

Calling a bet:
Expected value of calling a 5\$ bet in a 20\$ pot with 19% equity.
EV=0.19*(20+5) - 0.81*5
EV=4.75 - 4.05
EV= +\$0.7

Fold equity:
Ammount of fold equity needed to make a 3-bet push preflop profitable. The blinds are 1/2 and there is a raise to \$8. We have a stack of \$25 and expect to have 27% equity if called.
To find break even set EV=0. (Both players are outside the blinds)
0=P_fold*(8+1+2)+(1-P_fold)*(0.27*(1+2+25+25)-25)
0=P_fold*11+(1-P_fold)*(-10.69)
0=P_fold*11 - 10.69 +10.69*P_fold
10.69=21.69*P_fold
P_fold=0.493 =>49.3% of the times he needs to fold.

Purebluff FE:
Raising a cBet with 0% equity if called. Pot is \$10 and villain cbets \$7. We raise his bet to \$20
To find break even set EV=0.
0=P_fold*(10+7) - (1 - P_fold)*20
0=P_fold*17 - 20 + P_fold*20
20=P_fold*37
P_fold=0.54 =>54% of the times he needs to fold.

Tournament maths

M-factor:
M on a table with 9 players 25/50 and 5 ante with 2200 chips.
M=2200/(50+25+5*9)=18.33

Effective M-factor:
5 Players left on the table with 75/150 and 20 ante with 2200 chips.
M=2200/(150+75+20*5)=6.78
EM= 6.78*(5/10)=3.39

Effective bb:
9 Players on a table with blinds of 250/500 and 50 ante.
Ebb=2*(500+250+50*9)/3
Ebb=800
• Gold
Joined: 01.04.2009
Sticky imo. Thnx
• Bronze
Joined: 09.01.2012
great post