Basic Probabilty Questions

[TrainHardDieHard]

I'm not sure how to solve for these questions, so please provide an explanation + math + the answer =]

In hold'em, what is the probability of hitting a pair with any random hand on the flop? What is the probability of hitting a pair by the river?

How many possible card combinations are there for texas hold em? I got 1320 because I know there is a 1/220 chance of getting AA, and there a 6 possible AA combinations. 6 x 220 = 1320. If this is right, give me another method of solving it, and if it's wrong, please correct it. Thanks.

[AaronBrown]

If you have two different cards in your hand, there are six cards in the deck that can pair you, and 44 that do not pair you.

C(44,3) = 13,244 flops give you no pair
C(44,2)*C(6,1) = 5,676 flops give you one pair
C(44,1)*C(6,2) = 660 flops give you two pair or trips
C(6,3) = 20 flops give you a full house or quads

Add them up and you get C(50,3) = 19,600, the number of possible flops. If you don't know the "C" notation for the Choose function (Combin in Excel), I can explain it.

To solve by the river, you need to do the same thing as above, working from:

C(44,5) = 1,086,008 boards do not pair either card in your hand
C(44,4)*C(6,1) = 814,506 boards pair one card
C(44,3)*C(6,2) = 198,660 boards give you two pair or trips
C(44,2)*C(6,3) = 18,920 boards give you a full house or quads
C(44,1)*C(6,4) = 660 boards give you four matching cards, either quads and a wasted pair, or two trips that you'll use for a full house
C(6,5) = 6 boards have all five board cards matching your hole cards, so there is a full house on the board, but you'll have quads and wasted trips

That adds up to C(50,5) = 2,118,760 possible boards.

Good logic, but the chance of AA is 1/221 (220 to 1). 6 x 221 = 1,326. Another way to get this is 52*51/2. There are 52 cards for your first card, 51 for your second, but you have to divided by two because Ah 7s is the same hand as 7s Ah and you don't want to double count.

Another way to do it is to say there are 13 pairs, each one comes up 6 ways, for 6 x 13 = 78 hands. There are 13 x 12/2 = 78 suited hands, each one comes up 4 ways, 4 x 78 = 312. Each of those suited hands also comes in 12 unsuited versions, 12 x 78 = 936. 78 + 312 + 936 = 1,326.

[tmtmdeluca]

i got a probabilty question i have been playing for 2 years and have seen the same ammount of hands live as ive seen online the only differance is ive seen about 2000 bad beats live and 20000 online. what is the probabilty that this can happen.

[metsandfinsfan]

[ QUOTE ]
i got a probabilty question i have been playing for 2 years and have seen the same ammount of hands live as ive seen online the only differance is ive seen about 2000 bad beats live and 20000 online. what is the probabilty that this can happen.

[/ QUOTE ]

zero. Online people may be more likely to play garbage cards since they are anonymous ... so more bad beats can theoritically happen
but no online poker is not rigged