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I was going through an article where it's written:

"For example, if you hold two hearts, and there are two on the flop, you have nine outs to hit your draw, giving approximation of 18 percent to hit on the turn, or an 36 percent to hit by the river. This shortcut can be used in conjunction with pot odds to assess if your draw is worth continuing with."

I didn't understand how this 18 and 36 percent are calculated. If I have 4 hearts out of 47 cards and 9 outs left to hit at the turn, 9/47 = 19% approximately. If I don't hit on the turn, then at the river it should be 9/46 = 13% approximately. Then how is it 18% and 36%? Am I calculating it wrong?

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you are not calculating it wrong, the article states that 18% and 36% is a shortcut. the author of the article counts each out as 2% for each remaining street after the flop. so if there are 9 outs to a flush draw, there is (9*2 =) 18% chance to hit the flush on the turn, and another 18% chance to hit it on the river, giving 36% to hit the flush before showdown.

this is simply a fast way of calculating the percentage that you will make your hand at the table, rather than having to think about what 9/46 is.

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    i did not understand it properly, In the River the chances should be less as our probability is decreasing to make the Best 5 combination.So how its increasing to 36 % at the river ?
    – Max456
    Oct 2, 2019 at 3:33
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    36% is by the river (not at the river), so it includes both turn and river cards. The approximation is 2% per out per street, so 9 outs is 18% per street, which is approximately 36% for 2 streets.
    – sakon
    Oct 2, 2019 at 8:41
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The author is using a rule-of-thumb approximation. Your exact probability of hitting the turn is, as you say, 9/47, or about 19.15%. Your probability of hitting the turn OR the river is equal to (1 - (prob. of missing both turn and river)), or (1 - (38/47 * 37/46)), or 756/2162, or about 34.97%

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