Poker Mathematics - Part 1 - Ratios, Fractions and Percentages
This series will examine the mathematics supporting decisions at the poker table.
It is important for all players to have a solid grasp of these basic fundamentals as a minimum requirement for developing skills, improving long term profit.
The definition of Good Poker The ability to accurately quantify, or estimate, the % chance of various actions by opponent(s) and use mathematics to determine the line that will have the highest possible average rate of return.
It is a 2 part process: 1.
Anticipate your opponent's actions with good assumptions (improve with experience) 2.
Find the best line using mathematics This process is the best route to achieve optimum profit over the long term.
The level of knowledge (outside this series) can be expanded by using the traditional path via forums, asking questions and receiving a wide variety of views.
Ratios, Fractions and Percentages The relationship between these 3 statistics is very important.
Ratios A ratio describes one thing in comparison to another To convert a ratio to a fraction, ADD both numbers together to find the whole, for example: A ratio of 2:1 has a total of 3 chances.
The FIRST event will happen 2/3 of the time and the SECOND event will happen 1/3.
Fractions A fraction describes something as part of a whole To convert a fraction to a ratio, SUBTRACT the first number from the second number to find what amount IS NOT the first event, for example: A fraction of 1/3 has 2 occasions it does NOT happen.
This figure is the ratio, in this case 2:1 Percentages A percentage describes the same thing as a fraction but the whole is 1.
0 or 100% To convert a fraction to a %, DIVIDE the first number by the second number and multiply by 100, for example: A fraction of 1/3 = 0.
33 = 33% To convert a % to a fraction, DIVIDE the % by 100 to find out the portion of the whole you will have for 1 event, for example: 33% = 33/100 = 1/3 The % chance for 1 card to come This calculation is important for decisions on the flop or turn, where the % chance of a good card on the next street is critical in making bet, call or fold decisions.
Next Street To find the % chance for 1 card to come, DIVIDE the number of cards of that type by the number of unknown cards (pre-flop = 50, flop = 47, turn = 46), for example: The chance of an Ace on the turn if none has appeared in your hole cards or on the flop is 4/47.
Turn and River The formula for multiple chances (turn and river) is: 1 - (c1/u1)*(c2/u2) where c = chances of failure and u = unknown values.
We subtract the chances of the cards NOT being of the type required from 1.
Using the Ace example above, the formula would be: 1 - (43/47)*(42/46)
It is important for all players to have a solid grasp of these basic fundamentals as a minimum requirement for developing skills, improving long term profit.
The definition of Good Poker The ability to accurately quantify, or estimate, the % chance of various actions by opponent(s) and use mathematics to determine the line that will have the highest possible average rate of return.
It is a 2 part process: 1.
Anticipate your opponent's actions with good assumptions (improve with experience) 2.
Find the best line using mathematics This process is the best route to achieve optimum profit over the long term.
The level of knowledge (outside this series) can be expanded by using the traditional path via forums, asking questions and receiving a wide variety of views.
Ratios, Fractions and Percentages The relationship between these 3 statistics is very important.
Ratios A ratio describes one thing in comparison to another To convert a ratio to a fraction, ADD both numbers together to find the whole, for example: A ratio of 2:1 has a total of 3 chances.
The FIRST event will happen 2/3 of the time and the SECOND event will happen 1/3.
Fractions A fraction describes something as part of a whole To convert a fraction to a ratio, SUBTRACT the first number from the second number to find what amount IS NOT the first event, for example: A fraction of 1/3 has 2 occasions it does NOT happen.
This figure is the ratio, in this case 2:1 Percentages A percentage describes the same thing as a fraction but the whole is 1.
0 or 100% To convert a fraction to a %, DIVIDE the first number by the second number and multiply by 100, for example: A fraction of 1/3 = 0.
33 = 33% To convert a % to a fraction, DIVIDE the % by 100 to find out the portion of the whole you will have for 1 event, for example: 33% = 33/100 = 1/3 The % chance for 1 card to come This calculation is important for decisions on the flop or turn, where the % chance of a good card on the next street is critical in making bet, call or fold decisions.
Next Street To find the % chance for 1 card to come, DIVIDE the number of cards of that type by the number of unknown cards (pre-flop = 50, flop = 47, turn = 46), for example: The chance of an Ace on the turn if none has appeared in your hole cards or on the flop is 4/47.
Turn and River The formula for multiple chances (turn and river) is: 1 - (c1/u1)*(c2/u2) where c = chances of failure and u = unknown values.
We subtract the chances of the cards NOT being of the type required from 1.
Using the Ace example above, the formula would be: 1 - (43/47)*(42/46)