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Texas Hold'em Common Card Drawing Probability Shortcut Formula

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Post time 11-5-2024 10:27:30 | Show all posts |Read mode
Formula for calculating the probability of drawing cards after the flop:
P = N × 4 (N < 10)
P = N × 3 + 9 (N ≥ 10)
Where P is the probability of drawing a turn or river card, and N is the number of cards drawn.

Formula for calculating the probability of drawing cards after the turn:
P1 = N × 2 (N < 4)
P1 = N × 2 + 1 (4 ≤ N < 12)
P1 = N × 2 + 2 (N ≥ 12)
Where P1 is the probability of drawing a turn card, and N is the number of cards drawn.

Formula for calculating the probability of drawing cards after the river:
P2 = N × 2 (N < 3)
P2 = N × 2 + 1 (3 ≤ N < 9)
P2 = N × 2 + 2 (9 ≤ N < 15)
P2 = N × 2 + 3 (N ≥ 15)
Where P2 is the probability of drawing a river card, and N is the number of cards drawn.

For a pocket pair, the probability of flopping a set is: 12% or 1 in 8
For the turn and river, it's 8.4% or 1 in 10.9
For the turn alone, it's 4.2% or 1 in 22.8
For the river alone, it's 4.2% or 1 in 22.8

For AK as pocket cards, the probability of flopping a pair is: 32% or 1 in 2.7
For the turn and river, it's 24% or 1 in 4.2
For the turn alone, it's 13% or 1 in 7.7
For the river alone, it's 13% or 1 in 7.7

For two suited cards as pocket cards, the probability of flopping a flush is: 11% or 1 in 8
For the turn and river, it's 35% or 1 in 1.9
For the turn alone, it's 19% or 1 in 4.3
For the river alone, it's 19% or 1 in 4.3

For flopping an open-ended straight draw, the probability for the turn and river is 31.5% or 1 in 2.2
For the turn alone, it's 17% or 1 in 4.9
For the river alone, it's 17% or 1 in 4.9

When there are three cards of the same suit on the table and your pocket cards are Kx suited, the probability of losing to Ax suited is 6%, or odds of 16 to 1 in your favor.

The probability of getting two suited pocket cards is 23%, or odds of 1 in 3.

After the flop, there are 47 unseen cards, and after the turn, there are 46. So, you have two chances to get the card you're hoping for. Use the following formula to calculate the probability of drawing a card:

% = 100 [1 - (47 - N) (46 - N) / (47 × 46)] = 100 [1 - (47 - N) (46 - N) / 2162]
Where % is the probability of drawing the desired card on the turn and river, and N is the number of desired cards after the flop.

After the turn, there are only 46 unseen cards, so the probability calculation formula is:

% = 100 (M / 46)
Where % is the probability of drawing the desired card on the river, and M is the number of desired cards after the turn.

Conversion of probability to odds:
Odds = % : (100 - %)
For example, if you have a flush draw after the flop (missing one card for a flush), the probability of hitting a flush on the river is:
Odds = 19.6 : (100 - 19.6) = 1 : 4.1
This type of odds is not recommended for river betting.
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Post time 13-5-2024 07:39:43 | Show all posts
You can explore various algorithms to understand them better.
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