The other day we keep the sets, now we go a step further and look at the quads (poker).
First, let's see how many quads come out in 7 cards (2 and 5 our community): Merge
52 cards in groups of 7 to 7, C52, 7 = 133 784 560 different groups, this is the number of possible events. The number of events for ables is to the provisions of the type:
QQQQXXX
(this is a scheme, do not have to leave in that order)
where X can be any letter other than the Q. That tells us that the 48 remaining cards can be combined in groups of 3, so C48, 3 = 17 296 positive events. Of course that is just to make quads Q, as there are 13 possible quads is multiplied x13, giving us 224,848 favorable events. So the prob of a quad out with 7 cards is 224.848/133.784.560, or what is the same as a quad every 595 hands. But does that mean that I'm catching quads every day? Man, if with every hand you're dealt (whether or not to pp) VPIP you 100%, 100% saw flop = true and 100% of went to river, of course you should leave it. Notice Some of these quads have been on the board without any card you use.
-Ya but ... I, I'm pregnant, I have the craving to know how many quads pillared using my two hole cards.
"Honey, would have preferred to buy an ice cream. Let's see:
Each pair has 6 ways to order, as there are 13 pp 6x13 = 78 different ways to be pp. The number of possible events preflop, as we saw, remains C52, 2 = 1326. So if I have QQ preflop, the boards that take away the cravings are like:
QQXXX
The number of possible events are 50 cards of 5 in 5: C50, 5 = 2118760
The number of favorable events are 48 cards of 3 in 3: C48, 3 = 17 296 cases
intersect the event postflop preflop with the event, we have:
(78/1326) * (17,296 / 2118760) which gives more or less than 0.05%, which is the same as 1 once every 2083 hands.
All this is fine, but ... What if for some reason sidereal astrology-hypnotic-mecagoenelcicloreproductivodelmejillóncebra-eclectic-sleepwalker-hermeneutic-notedejesabiertalatapadelbáter-bizarre- chirripitifláutico-Sensory ... I want to know how many quads of 8 or higher I will catch using the two hole cards?
Then all you have to change is to reduce the pairs preflop, instead of 13 is 7, (now 6 * 7 = 42) and the calculation is:
(42/1326) * (17 296 / 2,118,760) = 0.03% approx. That is, 1 out of every 3868 hands. As always, this would be if each of 8 or higher pp 100% we saw flop = true and 100% of went to river.
I searched the gúguel quad and the only interesting thing I get is this (LOL, and look Pacocha):
Caught my attention because it seems an odd way to drive a quad (I usually slowplayeo quads on the flop). And the girl has no knee pads or helmets, or any kind of protection, flip-flops even obey the laws of Occupational Health and Safety (I doubt bearing steel soleplate anticlavos). C'mon, it's not a good example for children.
First, let's see how many quads come out in 7 cards (2 and 5 our community): Merge
52 cards in groups of 7 to 7, C52, 7 = 133 784 560 different groups, this is the number of possible events. The number of events for ables is to the provisions of the type:
QQQQXXX
(this is a scheme, do not have to leave in that order)
where X can be any letter other than the Q. That tells us that the 48 remaining cards can be combined in groups of 3, so C48, 3 = 17 296 positive events. Of course that is just to make quads Q, as there are 13 possible quads is multiplied x13, giving us 224,848 favorable events. So the prob of a quad out with 7 cards is 224.848/133.784.560, or what is the same as a quad every 595 hands. But does that mean that I'm catching quads every day? Man, if with every hand you're dealt (whether or not to pp) VPIP you 100%, 100% saw flop = true and 100% of went to river, of course you should leave it. Notice Some of these quads have been on the board without any card you use.
-Ya but ... I, I'm pregnant, I have the craving to know how many quads pillared using my two hole cards.
"Honey, would have preferred to buy an ice cream. Let's see:
Each pair has 6 ways to order, as there are 13 pp 6x13 = 78 different ways to be pp. The number of possible events preflop, as we saw, remains C52, 2 = 1326. So if I have QQ preflop, the boards that take away the cravings are like:
QQXXX
The number of possible events are 50 cards of 5 in 5: C50, 5 = 2118760
The number of favorable events are 48 cards of 3 in 3: C48, 3 = 17 296 cases
intersect the event postflop preflop with the event, we have:
(78/1326) * (17,296 / 2118760) which gives more or less than 0.05%, which is the same as 1 once every 2083 hands.
All this is fine, but ... What if for some reason sidereal astrology-hypnotic-mecagoenelcicloreproductivodelmejillóncebra-eclectic-sleepwalker-hermeneutic-notedejesabiertalatapadelbáter-bizarre- chirripitifláutico-Sensory ... I want to know how many quads of 8 or higher I will catch using the two hole cards?
Then all you have to change is to reduce the pairs preflop, instead of 13 is 7, (now 6 * 7 = 42) and the calculation is:
(42/1326) * (17 296 / 2,118,760) = 0.03% approx. That is, 1 out of every 3868 hands. As always, this would be if each of 8 or higher pp 100% we saw flop = true and 100% of went to river.
I searched the gúguel quad and the only interesting thing I get is this (LOL, and look Pacocha):
Caught my attention because it seems an odd way to drive a quad (I usually slowplayeo quads on the flop). And the girl has no knee pads or helmets, or any kind of protection, flip-flops even obey the laws of Occupational Health and Safety (I doubt bearing steel soleplate anticlavos). C'mon, it's not a good example for children. 
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