Bet Evaluation without Odds

cuffslurp · Dec 30, 2008

For the mathematically challenged, learning to estimate poker odds can be a nightmare. The math may be simple enough, but the calculations are often too difficult to perform under time restraints. Poker expert Phil Gordon has tried to remedy this situation by introducing the rule of 4 and 2 – a valuable tool to determine the chances of making your hand. Regretfully, it can still be a hassle to evaluate your bet, because of the mental leap between percentages and odds. Moreover, division can be a tricky operation to carry out – as opposed to multiplication.

After some research, I have found a way to evaluate bets using simple addition and multiplication. First, you apply Gordon’s rule, i.e. multiply your outs by 4 or 2, for the chance of making your hand after two or one cards, respectively. Then look up the resulting percentage in the following easily memorized table:

Code:

 %     n 
---------
50     2
33     3
25     4                 Notice how % x n = +/- 100
20     5                 
17     6                 The table simplifies what would have 
14     7                 been a time-consuming division.
13     8
11     9
10    10
 9    11

Now, multiply your bet by n – the result is the minimum size of the pot if you want to break even. Ideally, you’ll want the pot at showdown to be bigger than the projected break-even pot. Note that this final pot includes all bets from all rounds – yours and your opponent’s.

For example:

You’re in a $2-$4 Limit poker game, at the turn. The current pot contains $14, and you predict the final pot will contain $30. You’re one suited card short of a flush, so you have 9 outs – which means your chance to win is about 18%. You multiply your $4 bet by 6, for a projected break-even pot of approximately $24. Conclusion: your bet is justified.

heyyou01 · Dec 30, 2008

Thats a good one i will use this one when i need some help

riabylaw · Dec 30, 2008

I always have problems figuring this out fast. Maybe this will help me. Thanks.

cuffslurp · Dec 30, 2008

Another example.

Flop

You have 5 outs.

Gordon's Rule of 4

5 x 4 = 20%

The chances of making your hand by the river are 20%.

Table

Code:

20% corresponds to 5, so n = 5.

Break-Even Pot

Your bet is $4.

$4 x n = $4 x 5 = $20

Final Pot

There is currently $8 in the pot from your opponents.

With your bet, that amounts to (at least) $12 in the final pot.

Conclusion

You won't be able to break even.

$12 < $20

You should fold.

Stu_Ungar · Dec 31, 2008

For the mathematically challenged, learning to estimate Poker odds can be a nightmare. The math may be simple enough, but the calculations are often too difficult to perform under time restraints. Poker expert Phil Gordon has tried to remedy this situation by introducing the rule of 4 and 2 – a valuable tool to determine the chances of making your hand. Regretfully, it can still be a hassle to evaluate your bet, because of the mental leap between percentages and odds. Moreover, division can be a tricky operation to carry out – as opposed to multiplication.

After some research, I have found a way to evaluate bets using simple addition and multiplication. First, you apply Gordon’s rule, i.e. multiply your outs by 4 or 2, for the chance of making your hand after two or one cards, respectively. Then look up the resulting percentage in the following easily memorized table:

Code:
% n ---------50 233 325 4 Notice how % x n = +/- 10020 5 17 6 The table simplifies what would have 14 7 been a time-consuming division.13 811 910 10 9 11
Now, multiply your bet by n – the result is the minimum size of the pot if you want to break even. Ideally, you’ll want the pot at showdown to be bigger than the projected break-even pot. Note that this final pot includes all bets from all rounds – yours and your opponent’s.

For example:

You’re in a $2-$4 Limit Poker game, at the turn. The current pot contains $14, and you predict the final pot will contain $30. You’re one suited card short of a flush, so you have 9 outs – which means your chance to win is about 18%. You multiply your $4 bet by 6, for a projected break-even pot of approximately $24. Conclusion: your bet is justified.

WTF!!!

If you are going to refer to a table.. then why not just have a table of outs to odds???

Why bother calculating outs to precentages and then using a table to lookup percentages to odds???

It may be aimed at the mathmatically challanged, but could only be sold to the logically impaired!! LOL

This might be handy

http://www.texasholdem-poker.com/odds_chart

cuffslurp · Dec 31, 2008

Stu_Ungar said:
Why bother calculating outs to precentages and then using a table to lookup percentages to odds???

The numbers in the second column of the table are not odds. They are the result of dividing 100 by the chance to make your hand.

For example:

The chance of making your hand is 20%.

So, to break even in the long run, your share in the pot cannot exceed 20%.

What should be the minimum size of the pot in this case?

20% x 5 = 100%

Let's say your bet is $4.

$4 x 5 = $20

The projected break-even pot is $20.

Bet Evaluation without Odds

In summary, there are two calculations to be performed:

1) The chance of making your hand.

Most people seem to prefer calculating odds in stead of percentages, but percentages offer the advantage that you can use Gordon's rule of 4 and 2.

2) The size of the break-even pot.

Calculating pot odds is kind of illogical, since odds are about probability, and unless you include implied bets, calculating pot odds has nothing to do with probability.

By calculating pot odds you wish to find out what the ratio is between your bet(s) and your possible winnings. Pot odds are called pot odds, and not pot ratio, because they're meant to be compared to the odds of making your hand.

Anyhow, it seems more logical to me to translate the chance of making your hand to a projected break-even pot, than to translate the actual pot to odds. Of course, you can do it either way, and the result will be the same.

Stu_Ungar · Dec 31, 2008

Calculating pot odds is kind of illogical, since odds are about probability, and unless you include implied bets, calculating pot odds has nothing to do with probability

Anyhow, it seems more logical to me to translate the chance of making your hand to a projected break-even pot, than to translate the actual pot to odds. Of course, you can do it either way, and the result will be the same.

If the results are the same, how can the use of pot odds be illogical?

cuffslurp · Dec 31, 2008

Stu_Ungar said:
If the results are the same, how can the use of pot odds be illogical?

Well, maybe not "illogical" in the strict sense - it's just kind of counterintuitive to think of pot contents as odds in stead of money. On the other hand, viewing win percentages as cues of what kind of money you need to win to break even, seems perfectly natural.

You ask yourself: "how big does the pot need to be for me to call or raise?" - the answer is the projected break-even pot. Then you can start thinking about implied bets, i.e. speculating as to how big the final pot will be.

Stu_Ungar · Dec 31, 2008

"how big does the pot need to be for me to call or raise?"

TBH this has more to do with chip ratio of chip stack to the blinds of both you and your opponent rather than the actual figure of cash in the pot.

cuffslurp · Dec 31, 2008

Stu_Ungar said:
TBH this has more to do with chip ratio of chip stack to the blinds of both you and your opponent rather than the actual figure of cash in the pot.

You mean calling or raising depends mostly on other factors than the pot size?

True, but people do take the pot size into account. I'm just suggesting an alternative way to link the chances of making your hand to the pot size.

This does not affect other strategic considerations.

Stu_Ungar · Dec 31, 2008

You mean calling or raising depends mostly on other factors than the pot size?

Yes definately, especially if there are still future betting rounds left. Pot size is definately a factor but its as importent as may other factors which also need to be assessed.

True, but people do take the pot size into account. I'm just suggesting an alternative way to link the chances of making your hand to the pot size.

What I dont understand is why you would want to get away from odds and calculate them indirectly by looking at the break-even point of a pot.

Im not even sure why it is easier for you to calculate one and not the other. Thats the bit I just dont understand. It requires the same mathmatical operations to do either.

If it works for you then thats good, but I cant see the advantage.

The disadvantage would be that everytime you read a staratagy based on poker maths, you will have to convert it as the convention is to talk in terms of odds rather than future pot size.

cuffslurp_ · Dec 31, 2008

Let's run through my original example again:

You’re in a $2-$4 Limit Poker game, at the turn. The current pot contains $14, and you predict the final pot will contain $30 (including $4 bet). You’re one suited card short of a flush, so you have 9 outs.

Approach 1: Odds

There are 9 cards out of the remaining 46 cards that will make you win.

46 - 9 = 37

37 cards will make you lose.

Your odds are 37 to 9.

37 / 9 = ?

Wait ...

9 x 4 = 36

Your odds are about 4 to 1.

Your bet is $4, and the final pot $26 (excluding $4 bet).

26 / 4 = ?

Wait ...

6 x 4 = 24

The pot odds are about 6 to 1.

6 to 1 > 4 to 1

Your bet is justified!

Approach 2: Percentages

According to Gordon's rule of 2 ...

9 x 2 = 18

... your chance of making your hand is 18%.

100 / 18 = ?

Wait ...

17 x 6 = 100

You need to win 6 times your bet to break even.

4 x 6 = 24

The break-even pot is $24.

Your bet is $4, and the final pot $30 (including $4 bet).

$30 > $24

Your bet is justified!

Differences

1) In my approach, the actual pot isn't used for any calculations - it's just compared to the break-even pot in the end. Note that because I'm not interested in the pot odds against me, I can include my current bet into the final pot.

2) Odds calculations have a substraction and two disivions, my percentages calculations have one division and two multiplications. Arguably, division is the most difficult operation, so ...

Stu_Ungar · Dec 31, 2008

Approach 2: Percentages

According to Gordon's rule of 2 ...

9 x 2 = 18

... your chance of making your hand is 18%.

100 / 18 = ? The correct sum here is (100 - 18) / 18 or roughly 80 / 20

Wait ...

17 x 6 = 100 I think the 6 here came from your table in the origional post (see I am reading what you are saying.. I dont agree with it being easier but I am reading it) Remember you multiply your bet size by this figure of 'n'. You use the percentage to look up the value of 'n' from the table.

in my first post I posed the question why not have a table showing outs to odds.. negating any mathmatics in working out the strength of the drawing hand.. you havnt reall taken that on board.. you insist on working out percentages and then cross referncing these percentges to the value of 'n'.. To make your own method easier why not have a table of outs to 'n' values --- this was my origional point of the method proposed being increadably illogical (to make the maths easier you are doing some maths and then using a table.. wouldnt it be easier if you just used a table???)

You need to win 6 times your bet to break even. No, just over 4 will do it.. its a flush draw and the odds are just over 4:1 (remember you calculated this in the example you did before using odds) 'n' is just an itermediate step in your process.

4 x 6 = 24

The break-even pot is $24.

Your bet is $4, and the final pot $30 (including $4 bet).

$30 > $24

Your bet is justified!

Its just ironic that you got the maths right using the method you find illogical.

TBH once you get more familiar with outs to odds, you just learn them and dont really calculate the hand odds anymore. There are only about 20 to learn, after about 15 they are just fractionally lower than the previous and all under 2:1.

Personaly I'd stick with the traditional method.. in the longrun you will find it easier.

For me to do the same thing.. I look at the pot size, and divide it by the bet i have to call.. I get a pot odds figure. Say 6:1

I just know that 9 outs gives me just over 4:1 (you could use a table for this to begin with)

Here is such a table http://www.texasholdem-poker.com/odds_chart?chance_format=odds_against&decimals=2

so I compare 6:1 to 4:1 and then know I am in an situation with correct odds.

Its not as complicated once you start remembering odds.

I think its very good that you are taking the time to figure stuff out for yourself, its something that I do all of the time. I think it makes you a much better player because you will have a deeper understanding than someone who blindly excepts what they are told. Often I find that I my initial idea was wrong.. figuring that out also increases my knowlege. However there is no need to reinvent the wheel!!

Stu_Ungar · Dec 31, 2008

by the way instead of using (100-18) / 18 you can also use (100 / 18) - 1

cuffslurp · Dec 31, 2008

Stu_Ungar said:
Its not as complicated once you start remembering odds.

Thank you. You have made me see the error of my ways.

One more question, though.

If I understand correctly, the following equation needs to be true:

Code:

 winnings    
 -------- > odds against winning
   bet

But what if I'm not confident in my ability to quickly divide the predicted winnings by my current bet?

Would the following, mathematically derived equation be good, too?

Code:

 winnings > bet x odds against winning

In that case, I only have to memorize the odds, like you said.

Stu_Ungar · Dec 31, 2008

No probs

Yeah that would work.

I would still suggest looking at it in the form of odds.. once you get better at that you will be able to see an opponent make a bet and know the odds he was getting, thus determine how much he chases draws or how he sees players in terms of implied odds..

But for the purposes of seeing whether or not you are getting correct pot odds to call.. yes it is correct.

The other thing to remember is you dont have to be 100% exact on calculating pot odds, by using the rule of 2 and 4 you introduce some inacuracy into the calculating of the hand odds.. but its not a problem, its a good aproximation of the hand odds.

The same is true of pot odds, with the situation above where you got 6:1 pot odds and hand odds of a little more than 4:1, you would have to seriously over aproximate the pot odds to get a figure which would lead you to the wrong decision.

Say you are faced with calling a 430 bet for a pot of 1560.. its about 4:1, because the denominator (430) was rounded down id say its a bit under the 4:1 maybe as low as 3.5:1.. its just a guess.

The actual answer is 3.62:1.. Im happy with thinking its a figure between 3.5 - 4 : 1 (just punched it into a calculator)

We are being offered 6:1 its no where near. - easy call

3.5:1 - Id probably still call .. its mathmatically incorrect, but its not that much of a mistake. And when playing thats probably as accurate as my maths is. - Im saying this just incase you are trying to be too accurate. Once you start calculating things beond half an odd.. i.e 2:1, 2.5:1, 3:1, 3.5:1 then its just overkill.

In the aboveexample I knew it was a bit under 4:1 so I opted for 3.5:1 It just seemed correct.. as it turned out it was good enough.

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