Common Mistakes Using Odds

By Greg Walker

As a regular cash game or tournament player, it is important that you are familiar with the mathematics of poker.

This involves working out the odds of each situation so that you can determine what the most profitable action will be. A good player will be able to take into account their pot odds, implied odds and even their reverse-implied odds when calculating their next action.

However, with all these calculations taking place, there are a few simple errors that can be made when trying to work out the correct odds in each situation. The top 3 common mistakes I see are:

1. Miscalculating the odds of draws.
2. Miscalculating percentage odds.
3. Misunderstanding the difference between ratios and probability.

1) Miscalculating the ratio odds of draws.

The most common mistake that even the best players make is working out the incorrect odds they have for a draw. Many players will look up and remember the odds of completing such draws like flushes and straights by the final river card. Whilst these figures may be correct, it will not be profitable to use these odds when you are calling a bet on the flop to try and complete your draw by the turn.

As already mentioned, many odds charts will give you the likelihood of completing a draw by the river, for example the chance of completing a flush draw after the turn and river have been dealt is roughly 2:1. However, if we are only using these odds to compare whether we should call a bet on the flop to try and make our hand by the turn, we are neglecting the fact that we may well face another bet on the turn to see the river.

When looking up the odds on draws, use the odds for the next card only when on the flop. Do not use the odds for completing your draw by the final card.

A bet on turn is not unlikely, and so our pot odds will be worsened by the fact that we will have to have called two sizeable bets instead of one on the flop. Therefore instead of using the odds to complete draws by the river, we should be using the odds to complete draws by the next card instead. Typically for flush draws, the odds of completion by the next card will be 4:1. So when on the flop:

• Odds of completing a flush by the turn: 4:1
• Odds of completing a flush by the river: 2:1

Ratio odds miscalculation example.

For example, if we are on the flop with a flush draw and our opponents bet $40 making the pot $120, we are getting 3:1 odds from the pot. Therefore this appears to make a call with 2:1 odds of completing our hand profitable. However, we don’t complete our hand on the turn and our opponent now bets $80 into the $160 pot, again giving us 3:1 odds.

The fact that our opponent has bet again has reduced our pot odds so much that it has made our call on the flop unprofitable. This is because if we now call the bet on the turn, we would have effectively paid $120 into what became a $200 pot, which changes our pot odds to 1.7:1.

Therefore by using the incorrect 2:1 odds on the flop we have made an incorrect call, and we would be losing money in the long run by making this play. However, if we had used the correct odds of making our hand by the next card instead of the final card, which are 4:1, we could have folded knowing that we had the wrong odds to play on and saved ourselves some money.

2) Miscalculating percentage odds.

Some players prefer to work out the percentage odds to determine whether or not to make a call instead of using the ratio method as above. However, there is a very basic mistake that is frequently made using this method, especially if you are already used to working with the ratio method.

The common mistake is not adding your own call into the total size of the pot when working out your percentage pot odds. With ratio odds it is something that you are not required to do, but with the percentage odds it is important that you do not forget to do so.

Always add your own call amount to the total size of the pot when working out percentage odds.

Percentage odds miscalculation example.

If your opponent bets $40 into an $80 pot, the total size of the pot after you have added together your opponent’s bet and your call will be $160.

Therefore your $40 call into the total pot of $160 would be worth 25% of that pot, therefore you can then use this 25% figure along with the chance of completing your hand to determine whether or not to call. This is the correct way to work out the odds.

The error is made when players do not add their own bet into the total pot size, so instead of coming out with a total $160 pot, they will be working with a $120 pot, as they have forgotten to add their own $40 into it. Therefore they will then work out the percentage of $40 out of $120, which works out to be 33%. This is quite far off the $40 out of $160 being 25%, and it could mean the difference between making a profitable or losing call to try and complete your draw.

3) Misunderstanding the difference between ratios and probability.

This mistake is far less of a problem, as you will rarely ever be required to mix odds and probabilities at the table when working out draws. However, it is useful to be aware of the differences in them. For example, having 1 in 4 odds of completing a draw is slightly different to having 4:1 ratio odds of completing a draw.

Ratio and probability figures in poker are different. A 4:1 ratio is not the same as a 1 in 4 fraction.

X in Y odds and X:Y (X to Y) ratios.

• 1 in 4. For every 4 times an event takes place, you will have the result you are after 1 time (out of those 4 trials).
• 4 to 1. For every 5 times an event takes place, you will have the result you are after 1 time and the unwanted result 4 times (so 5 trials in total).

The 1 in 4 odds takes place over 4 trials, where you will obtain the wanted outcome once and an unwanted outcome 3 times. Whereas in the 4:1 ratio odds, there are 5 trials, where you will obtain the expected outcome once, and an unwanted outcome 4 times.

As you can see, you have to add the ratio together to find the total number of trials, whereas the total number of trials is already given to you in the fraction format. Below is a simple table to help illustrate the differences between this particular set of odds.

	Wanted	Unwanted	# Trials
4 to 1	1	4	5
1 in 4	1	3	4

Conclusion.

There are numerous ways in which a player can slip up when using mathematics in poker. It is not uncommon to even have regular veteran players make these simple mistakes, so don’t be too concerned if you make a small mistake every now and then.

This article was written to try and help make you aware of the most common mistakes so that you can avoid them in the future. The more you play and work with odds, the better you will become at making precise and profitable decisions at the poker table, so get out there and play!

Go back to the awesome Texas Hold'em Strategy.

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