# Ratio vs Percentage in pots odds and hand odds

Firstly, I am confused in when do we use the word odds vs outs, so, pardon me if my words don't make sense at some point.

When trying to decide if I need to go in a hand or not (after the flop), here is what I do:

1 - Ratio method.

If there are 9 cards that will help me do my flush, and there are 5 cards that I know (3 on the table and the 2 I hold), there are 52 - 5 - 9 = 38 cards that won't help me and 9 that will do. So the hands odds are:

38:9 or 38/9:9/9 or approximately 4:1

On the other hand, if there are \$80 in pot, and my opponent bets \$20, means we need to bet \$20 to get \$100. That is:

100:10 or 10:1

So, the odds of the pot are bigger than the pots from the hand, so we should bet.

2 - Percentage method.

When using percentage, I use the rule of 2, so we would have:

9 cards would help me that is 18% of making the flush in the next hand.

But how do I calculate the percentage of the pot odds? And once I have that percentage, how do I decide if I have to go or should I fold?

• we need to bet \$20 to get \$100. That is: 100:10 or 10:1 -- No... it's 100:20 or 10:2 or 5:1. – mah Jun 4 '14 at 11:28

# I am confused in when do we use the word odds vs outs

Outs only refer to how many cards can come down on later streets which will improve a hand's absolute strength.

Odds refer to how likely it is an event will occur. In poker, we are frequently calculating pot odds, which tells us, if we call a bet, how often we need to win the hand for the call to be at least breakeven.

# But how do I calculate the percentage of the pot odds?

You basically did the calculation correctly, except you made a typo in the final calculation. There's \$100 in the pot and we need to call \$20, meaning we are getting 5:1 odds, not 10:1.

To convert this to a percentage, just use the following:

Pot Odds = ((Amount to Call) / (Amount to Call + Pot Size)) * 100
Pot Odds = (20 / (20 + 100)) * 100
Pot Odds = (20 / 120) * 100
Pot Odds = (1 / 6) * 100
Pot Odds = 16.67%

Or, more simply, since we are getting 5:1 odds... divide 1 by 5+1. 1/6 = 16.67%

# And once I have that percentage, how do I decide if I have to go or should I fold?

So, using pot odds we found out that we only need 16.67% equity to continue in the hand here. We have 9 outs to complete our flush draw. We can use the Rule of 4 and 2, which will allow us to closely approximate our equity at the table, in the following way:

On the flop, multiply your outs by 4 to get our equity on the flop.
On the turn, multiply your outs by 2 to get our equity on the turn.

So, on the flop, the rule of 4 tells us we have approximately 36% equity. On the turn, we have approximately 18% equity. So if the \$20 bet was made on the flop, it's a very easy call since we only need 16.67% equity to justify calling. If it was the turn, you aren't getting the immediate pot odds to justify calling but once you factor in implied odds, which is how many chips you can expect to make on later streets when your hand improves to a flush, it becomes an easy call since we only need 20% equity and we have 18%.

• Interesting. However, let me ask you something: I have heard that using the rule of 4 is not 'good'. It should always be used the rule of 2, whether in the flop or in the turn. Because when you multiply by 4 you are assuming stuff that will happen in other streets. Am I right on that assumption? And second question: When using ratio, you make the call if the odds of the pot are bigger than the hand. However, when doing percentage, you make the call if the percentage of the hand is bigger than the percentage of the pot. Why is different when using ratio than when using percentage? – Nobita Jun 4 '14 at 4:22
• Yes, some people might suggest not using the rule of 4 simply because it includes the chance that your outs will come on both the turn and river. Since you might not reach the river sometimes, it devalues the rule of 4. But if you keep this in mind and realistically estimate the likelihood of seeing both the turn/river, you can bounce between using either the rule of 4 or the rule of 2 on the flop. But just flat out saying "never use the rule of 4" is a bad plan. – Brent Morrow Jun 4 '14 at 8:18
• I'm not sure what you're asking about the difference between using ratios and percentages. When you count your outs on the flop/turn, you are doing so to determine what number to multiply using the rule of 4 and 2. You shouldn't be calculating the odds of your hand improving. It's irrelevant, unnecessary info to be calculating at the table. Count your outs, multiply by the rule of 4/2, and then you have your equity. If you have more equity than is needed according to the pot odds, continue in the hand. – Brent Morrow Jun 4 '14 at 8:22
• Thanks a lot for your comments. What I was saying about the difference between ratios and percentage is that: 1- If my ratio of hands are 4:1 and my ratio of pots is 10:1, since the pot ratio are bigger, you choose to continue. However, in 2 - If percentage of hands 36% is bigger than percentage of pot 10%, you continue. So as you see in one case you decide if hands (percentage) is bigger, and in the other if pot (ratio) is bigger. – Nobita Jun 4 '14 at 16:46
• I have a question. When doing the conversion you say that 1:5 => 20%. I have seen in several sites, the following 1:5 => 17% (thepokerbank.com/tools/odds-charts/ratio-percentage) - Any ideas why? – Nobita Jun 5 '14 at 3:51

I am learning the US is predominately ratio and outside the US percentage is commonly used.

## Convert Odds to Percentage

Odds are always with a :
1:1
2:1
3:1

Percentage / fraction
33% = 1/3
50% = 1/2

percentage = 100 / (odds + 1)
odds = (100 / percentage) - 1

fraction = 1 / (odds + 1)
odd = 1 / fraction + 1

the chance of pocket aces is 1/221 = 220:1

33% = 1/3 = 4:1
50% = 1/4 = 3:1
100% = 1/1 = 2:1

In 4 to 1 typically means 4 : 1

# Ratio

### Pot Odds / Ratio

It is not just number from percentage but it is upside down

pot size : amount you have to call

pot was \$80 and they bet \$20
\$100 pot and call \$20 = 5 : 1
You are risking \$1 to win \$5
Now the pot is \$120

### Hand Odds

(cards left - outs)/outs
If you have 8 outs on the turn then
(46-8)/8 = 4.75 : 1
or
(1 - fraction) / fraction
or (100 - percentage) / percentage

### Pot Odds Versus Hand Odds

If you are getting
Pot Odds > Hand Odds then call
Reward > Risk

Pot Odds (5:1) > Hand Odds (4:75) then you are getting immediate odds to call

If they bet was 1/2 the pot giving you 3:1 pot odds then you should not call 8 outs (unless you think you are getting good implied odds)

# Percentage same hand

\$80 + \$20 + \$20 = \$120

pot pct = 20 / 120 = 1 / 6

hand pct = 8 / 46 = 4 / 23 = 1 / 5.75

It is backward from odds as you need hand pct > pot pct to call

# Summary

Ratio may seem more complex but at the table it is way easier for me. Dealing with numbers > 1. 20 to win 100 is 5 : 1. 20 / (100 + 20) is 1/6 is just more work.