Basic Pot odds question

[nvflag]

1.) What are the odds of catching a flush when you have two suited cards and two of these same suits come out on the flop.

After the flop:

After the turn:


2.) what are the odds of completing your straight when you flop an open ended straight draw

after the flop:

after the turn:

3.) What are the odds of completing your straight when you are on an inside straight draw after the flop.

After the flop:

After the turn:

4.) You have a pocket pair before the flop. What are the chances of flopping a set ?

[SossMan]

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[Mike Haven]

1.) What are the odds of catching a flush when you have two suited cards and two of these same suits come out on the flop.

After the flop:

You have seen 5 cards. Of the 47 unknown cards, 9 are your suit, 38 aren't.

Odds are a way of saying you won't hit some number of times compared to the times you will hit. You won't hit 38 times, and you will hit 9 times, in the long run. So the odds that you will make your flush on the turn are written as 38 to 9, which is the same as 4.2 to 1, (dividing both numbers by 9). Another way of finding your chances of hitting on the turn is by saying you'll hit 9 times out of 47. For ease we like to know the conventional standard of how many times in a hundred we will hit. This is calculated simply by multiplying our 9 out of 47 by 100 like so: (9/47 x 100) = 19.15 and calling it "per cent" (per hundred) = 19.15%.

Of the 80.85% (100% - 19.15%) of the time that you don't make your flush on the turn you will make it (9/46 x 100) = 19.56% of the time on the river, which is 80.85 x 19.56% = 15.81% of the whole time.

Therefore, you will make your flush either on the turn or the river 19.15% + 15.81% = 34.96% of the whole time.

To change percentages to odds you have to use the system of (100 - 34.96)/34.96 = 65.04/34.96 = 1.86 to 1. If you take two cards to a four-flush on the flop, you will not flush 1.86 times for every once you do flush.


After the turn:

You have seen 6 cards now, so of the 46 unknown cards in the deck, as 9 of them are your suit, the odds that you will catch one of the 9 on the river come from the likelihood of you receiving 37 off-suiteds to 9 suited = 37/9 = 4.1 to 1.