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## Betting and Errors in Poker

If we break down betting to the very basics, there are two types of bet, or two reasons you bet:

• Value Bet: A bet with the goal of getting worse hand to call
• Bluff: A bet with the goal of getting a better hand to fold

To determine the appropriate type of bet to make, you need to ask yourself “What type of errors are my opponents (or is this particular opponent) making?”

If poker were a game like chess, we would analyze which types of bets are best based on your hand, your position, your chip stack, the board, etc…  In chess, moves can be analyzed regardless of your opponent.  In poker, this is not the case.  Whether you should be value betting or bluffing hinges on the errors being made by your current opponent(s).

Are you opponents putting chips in the pot with worse hands?  Are your opponents folding too often?  These questions help determine your reasons for betting.

#### Types of Errors

First, let’s look at the definitions of Type 1 Errors and Type 2 Errors and what these errors look like in the world of statistics.

Example:  You want to know if you are pregnant and you take a pregnancy test.  There are 4 potential outcomes:

• You are not pregnant and the test comes back negative.
• You are not pregnant and the test comes back positive.
• You are pregnant and the test comes back negative.
• You are pregnant and the test comes back positive.

Two of the above outcomes lead to correct results.  Let’s view this in a table:

 Not Pregnant Pregnant Negative Result Correct Result Positive Test Correct Result

The other two outcomes, which are blank in the table above, lead to errors (incorrect results). These errors are defined as:

• Type 1 Error: You are not pregnant and the test comes back positive – a false positive.  A Type 1 Error is the assertion of something that is absent.
• Type 2 Error: You are pregnant and the test comes back negative – a false negative.  A Type 2 Error is the failure to assert something that is present.

In table format:

 Not Pregnant Pregnant Negative Result Correct Result Type 2 Error – False Negative Positive Test Type 1 Error – False Positive Correct Result

In the pregnancy example, think about the consequences of each error type as it pertains to an individual (or a society). What are the implications of Type 1 Errors? What are the implications of Type 2 Errors?

#### Betting Errors

Looking at the basics of betting, we can create a similar table to model a simplified situation.  In this situation, you bet.  Your opponent either has a better hand or a worse hand, and either calls or folds.  See the errors that can be made by your opponent below:

 Opponent has a better hand Opponent has a worse hand Opponent Calls No Error Type 2 Error Opponent Folds Type 1 Error No Error

#### Bluff

When you bluff, you are counting on your opponent to make a Type 1 Error.  You are asserting something that is absent (a strong hand) and your opponent falsely believes you and folds.

If your opponents are waiting for strong hands and folding too often, they are making Type 1 Errors.

#### Value Bet

When you value bet, you are counting on your opponent to make a Type 2 Error.  You fail to assert strength (making your opponent sense weakness) and your opponent falsely believes you and calls.

If your opponents are calling too much or seeing too many rivers, they are making Type 2 Errors.

#### Are you helping your opponents correct their errors?

You need to take advantage of the types of errors your opponents are making.  As well, your bets should not encourage your opponents to correct their errors.

For example: drastic over-bets encourage players who make Type 2 Errors to play correctly and fold when otherwise they would have called a standard-sized bet with a weaker hand, giving you lots of value.

And, a player who makes Type 1 Errors will fold to standard-sized or over-sized river bets, but be encouraged to play correctly by calling smaller-sized bets.

Figure out which type of errors your opponents are making and then bet accordingly.

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