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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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## The Bet

Before I post this question, let me start by saying that I love a good bet.  My husband and I bet on everything — that is the only way chores get done in the house.  And, FYI: he is currently on 2 weeks of “diaper duty” for our 1-year-old since he lost 2 bets!  Don’t mean to rub it in or anything 😉  We are poker players… So here it comes:

Q:

I have a math question that I hope can help solve a \$5 bet I have with my friend Steve. It’s not advanced math by any means but Steve and I can’t seem to agree on who is right. First, a little background:

Our local driving range sells a medium bucket of balls for \$7 and \$9 for a large bucket. They offer a nice discount if a person buys a “punch card” that is good for 10 buckets of balls. Steve and I each pay \$70 for a card which is good for 10 large buckets of balls. It’s a \$20 savings for each of us! Another perk is if someone saves their cards and turns in 10 punched out cards (having spent \$700) they will receive a free card worth, in our case, 10 more large buckets worth \$70. Pretty cool!

Here’s what happened: Steve had saved 7 punched out cards and went to buy another. After he paid \$70 for his 8th card and mentioned that he only needed to buy 2 more cards to be eligible for his free card some guy who was near us and whom we didn’t know said “Hey, I’m moving out of town so I won’t need this punched out card that I’ve been saving” and he gave it to Steve.

As we were walking out to hit some balls I said to Steve, “Wow, that guy saved you \$70 towards your free card”. Steve disagreed. His reasoning was “what if I found 10 punched out cards that someone had lost and I turned them in to get my free card”? He said the free card is worth \$70 so by dividing the number of found punched out cards (10 cards) into the value of the free card (\$70) then each punched out card was only worth \$7. To Steve the card given by that unknown guy saved Steve only \$7. I told Steve that because of that gift card given to him he would end up paying only \$630 instead of \$700 to get his free card, therefore that guy saved him \$70.

So, can you explain who wins the \$5?