Let's say we have two hearts and there are another two on the flop. So, there are 9 hearts out of (52 minus our 2 minus the 3 on flop) 47 cards. We do not count our opponents' cards, as we do not know whether they have a heart on them or not.
To calculate the chance we have to complete our flush, we will do a little trick. We will calculate the chance not to complete our flush first, which is easier.
We will not complete our flush if the turn and river are both not a heart. The chance that this happens is 36/47 * 35/46 * 100%. Note that 36 out of 47 cards do not give a flush on turn, and 35 of 46 ( because a non heart was dealt previously ) do not give a flush on the river. This equals 58,28%.
So the chance for us to complete the flush obviously is 100%-58,28%=41,72%.
In Open Face Chinese Poker, these calculations are not so easy to make. After you are dealt your 5 cards, not only there are 8 cards to come for you instead of 2, but also there are 5 other open cards, for each opponent you have, on the table. But the biggest problem is that with every card that you will be dealt, your opponents will also be dealt another card that may or may not suit you.
With these conditions, its nearly impossible to try to figure out what is the exact chance to complete a flush draw after you are dealt your first 5 cards. To try to calculate the chance for completing a flush draw we must make an assumption. We will assume that we are dealt all the remaining cards right away without all the other players getting any. This way we simplify the problem at hand very much.
So, finally, lets try to calculate a problem. Let's say we are dealt 4 hearts, and we play heads up with another player who was dealt before us 2 hearts and 3 other cards.
Same as before, the chance not to complete the flush is:
35/42 * 34/41 * 33/40 * 32/39 * 31/38 * 30/37 * 29/36 * 28/35 *100%
This equals 19,94%. So the chance to make our flush is 80,06%.
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