Poker Mathematics - Basic Fundamentals

[sun137]

This is a link to the 2 threads in the MTT section. They probably should have been posted in the cash section with a link to the MTT area, but the link is here now because I believe cash game players who do not play MTT are missing out on the knowledge.

Poker Mathematics:

viewtopic.php?f=4&t=4499

Hand Ranges and Odds:

viewtopic.php?f=4&t=4481

[sun137]

The Rainbow Table was developed for MTT players to make decisions easier at the M Zone levels below Green. However the background working data used a comprehensive analysis of all hole card combinations against 10 different opponent ranges using Poker Stove to obtain summary information.

We all consider how much equity we have in a hand against an opponent's range in cash games, so I thought it may be helpful to post the more relevant detail and summary tables:






If you want to know the exact Poker Stove equity figures for each hand (from which the above summary tables were built), here they are:








If you want a summary of Phil Gordon's formula for the % chance of a PP being held by a player still to play behind you, here it is:



If we look at a simple summary of odds and SD equity, we can establish the minimum and maximum range of odds for any hand:

90% Equity............9/10 = 1/1.11..........an odds ratio of 0.11 : 1
80% Equity............8/10 = 1/1.25..........an odds ratio of 0.25 : 1
70% Equity............7/10 = 1/1.43..........an odds ratio of 0.43 : 1
60% Equity............6/10 = 1/1.66..........an odds ratio of 0.66 : 1
50% Equity............5/10 = 1/2.00..........an odds ratio of 1.00 : 1
40% Equity............4/10 = 1/2.50..........an odds ratio of 1.50 : 1
30% Equity............3/10 = 1/3.33..........an odds ratio of 2.33 : 1
20% Equity............2/10 = 1/5.00..........an odds ratio of 4.00 : 1
10% Equity............1/10 = 1/10............an odds ratio of 9.00 : 1

2 other important Equity/Odds numbers are:

33% Equity............3.33/10 = 1/3.00......an odds ratio of 2.00 : 1
25% Equity............2.50/10 = 1/4.00......an odds ratio of 3.00 : 1

The detailed tables confirm there are NO non-pair hands worse than 15% equity against the tightest range of 3.3%, or 18% for suited hands and this rises to 20% and 23% respectively against a 5.6% range (suited hands always have 3% more equity than unsuited hands).

If the worst trash hands are ignored, we can assume our hand will ALWAYS have at least 25% SD equity preflop, with a maximum odds requirement of 3.0 : 1, against ANY range of hands above 5%.

If the worst trash hands are ignored, we can assume out hand will ALWAYS have at least 33% SD equity preflop, with a maximum odds requirement of 2.00 : 1, against ANY range of hands above 7.4% (use this for TAG players)

If the worst trash hands are ignored, we can assume our hand will ALWAYS have at least 40% SD equity preflop, with a maximum odds requirement of 1.50 : 1, against ANY range of hands above 25% (use this for LAG players)

Note:

If you are playing against an opponent with a higher range than 7.4%, the odds increase by (roughly) 0.1 for every 3% increase in range. A T9s hand, for example, would improve minimum odds to 1.4:1 against an opponent with a range of 25% (up 0.6 for an 18% range increase).

OTHER IMPORTANT ODDS

The top 20% of hands do not require more than 2.0:1 (apart from KT/QJ/QT/JT, which require 2.3) against the tight 7.4% range.

ALL suited connectors have similar SE% and odds requirements from 2.5:1 upwards.

ALL unsuited connectors have similar SE% and odds requirements from 2.8:1 upwards.

If you have established a range of hands you use to play atm, look at the tables to give yourself an idea of potential pre-flop equity against Rock, TAG and LAG opponents. It is reasonable to treat any range over 40% as if it were a RANDOM hand (the 100% Range table).

You may find there are other hands you can safely add to your range, or there are hands you should exclude from your current playing range because they are too marginal.

Caution:

The above tables are PRE-FLOP Showdown Equity tables and should be used as a guide to establish initial opening ranges by position in your cash games. The parameters all change once the flop is dealt, but the tables can be a useful guide to all-in calculations.