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| Term | Definition |
|---|---|
| Community Card | Any of the 5 cards dealt face up on the table. |
| the Flop | The first 3 community cards. |
| the Turn |
The 4th community card.
( The stage of the game at which this card is dealt is also called "the Turn". ) |
| the River |
The 5th community card.
( The stage of the game at which this card is dealt is also called "the River". ) |
| Unseen Card |
Any card you have not yet seen. It has either been dealt ( face down ) to another player, or it could appear at the Turn or River. |
| Poker Hand |
Five or fewer cards which rank from
low to high in this order : one pair two pair three of a kind straight flush full house four of a kind straight flush royal flush |
| Out |
A single unseen card which, would significantly
improve your hand. It would either give you a poker hand, or if you already have a poker hand, it would give you one of higher rank. |
The Rule of 4:
After the flop but before the Turn, you can estimate
the probability that
either the Turn or River will
significantly improve your hand by simply
counting
the Outs and multiplying that count by 4.
The following chart shows the exact probability
( rounded to 3 decimal places ) that
either the Turn or the River ( or both ) will be
an Out.
Notice that this probability is approximately
equal to four times the number of Outs ( unless
there are more than 10 outs ).
| Nbr of Outs | Probability | 4 * Nbr Outs |
|---|
How can you find the exact probability that the Turn or the River ( or both ) will be an Out ?
Since what happens at the River depends upon the number of Outs and upon what happens at the Turn, the best way to solve this problem is to use an indirect approach -- find the probability of the complement of the event you are interested in and then subtract that probability from 1.
You can easily find the probability that neither the Turn nor the River is an Out. Then subtracting that probability from 1 will give you the probability that an Out will occur on the Turn or the River ( or at both times ).
Since you can see 5 cards ( 2 in your hand plus 3 in the flop ),
there are 52 - 5 = 47 unseen cards.
Let x = the number of Outs.
The number of ways in which the last two community cards can be chosen is the number of ways of choosing 2 things from 47 things ( = 47*46 / 2 ) , and the number of ways of choosing 2 cards that are not Outs is the number of ways of choosing 2 things from 47 - x things, which is (47 - x)*(47 - x - 1) / 2.
So, the probability that neither the Turn nor the River will
be an Out is
(47 - x)(46 - x) / (47 * 46) .
Thus the probability that the Turn or the River ( or both ) will be one of the x Outs is given by
| probability = [ 1 - |
(47 - x) * (46 - x)
(47 * 46) |
] * 100% |
Texas Holdem also has a Rule of 2 .
The Rule of 2:
After the Turn, the probability
that the River will be an Out is a
percentage whose size is approximately
2 times the number of Outs.
Reason:
If we let x be the number of Outs, then
the exact probability
is simply
x / 46 = ( x / 46 ) * 100%.
[ which equals x * ( 100 / 46 ) percent
= x * ( 2.17391... ) percent. ]
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Last Update: 18 October 2006
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