Counting outs question

This may well be a stupid question, but I'm gonna ask it anyway with the hope someone can correct my faulty logic.

There are a couple ways I count outs for holdem -- one by ratios and one by percentages. The first way I learned was a simplified (and slightly less accurate) way by percentages. The way I do it this way is to count outs (let's say it's 9 outs for the flush draw) and multiply by two and add two. That yields about a 20 percent chance to catch an out on the next hand (multiply by 4 to find out what the percentage is to catch it by the river).

The other (and more accurate) way is to memorize the ratio outs chart. For the flush example, there is a 4-to-1 chance of catching the out on the next card. Then what I do is to take the 4 and multiply it by the bet made to me. If the total is equal to or less than the total pot, then I have the odds to call.

For example, if the pot is $75, and a $25 bet is made (making the pot $100), I multiply the 4 (4-to-1 odds on the flush draw) by the bet (4x25=100). Since 100 is eqaul to the pot, I am in the odds to call.

There is obviously a discrepancy between the ratio and percentages I laid out. The first way yielded 20 percent pot odds, the second way yielded 25 percent.

Also, for example, consider 15 outs (a flush draw with two over cards)

The first way yields about 32 percent (15 times 2 plus 2), which is pretty accurate according to a pot odds calculator I checked (the actual percentage is 31.5). But the ratio is 2.1-to-1 (which is around 50 percent, no?). So what am I doing wrong here?

[BruceZ]

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This may well be a stupid question, but I'm gonna ask it anyway with the hope someone can correct my faulty logic.

There are a couple ways I count outs for holdem -- one by ratios and one by percentages. The first way I learned was a simplified (and slightly less accurate) way by percentages. The way I do it this way is to count outs (let's say it's 9 outs for the flush draw) and multiply by two and add two. That yields about a 20 percent chance to catch an out on the next hand (multiply by 4 to find out what the percentage is to catch it by the river).

The other (and more accurate) way is to memorize the ratio outs chart. For the flush example, there is a 4-to-1 chance of catching the out on the next card. Then what I do is to take the 4 and multiply it by the bet made to me. If the total is equal to or less than the total pot, then I have the odds to call.

For example, if the pot is $75, and a $25 bet is made (making the pot $100), I multiply the 4 (4-to-1 odds on the flush draw) by the bet (4x25=100). Since 100 is eqaul to the pot, I am in the odds to call.

There is obviously a discrepancy between the ratio and percentages I laid out. The first way yielded 20 percent pot odds, the second way yielded 25 percent.

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Both ways yielded 20%. 4-to-1 odds is 1/5 or 20%. For the exact probaility, divide 9 outs by 47 cards to get 19.1% or 4.2-to-1 odds.


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Also, for example, consider 15 outs (a flush draw with two over cards)

The first way yields about 32 percent (15 times 2 plus 2), which is pretty accurate according to a pot odds calculator I checked (the actual percentage is 31.5). But the ratio is 2.1-to-1 (which is around 50 percent, no?). So what am I doing wrong here?

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The actual percentage is 15/47 = 31.9% which is 2.1-to-1. 50% would be 1-to-1.

2.1:1 is the same as 1/3.1

Thanks!