a beginners question

[Checkov]

Can you help me with this poker math problem?

I have pocket 88's what's my probability of flopping a set?

Here's my math:

You have seen two cards and not seen 50. There are two more eights out of fifty

2 divided by 50 = .04 or 4% or 25 to 1. It will happen once every 25 times.

Now you have three chances so its = .12 or 12% which is the same as 8.3 to 1. It will happen once every 8.3 times it will happen.

Am I right so far?

Next.

I have pocket 88's what are the odds of getting a set after the river?

I have five chances of 4% so now it becomes 20%, or 5 to 1.

Am I on the right track?

Now ...

I have two kings - KK
Opponent Ted has two queens - QQ
Opponent Alice has two jacks - JJ
Opponent Ralph has two tens - TT

Over the next five community cards what are the percentages that my hand will not be beat? Will I win ?% of the time? What is the formula? If everyone has 20% chance of getting three of a kind, what is the formula to show the correct percentages for each hand winning after the next five cards appear. What is the percentage that my KK will remain the best hand after river. Assuming I put my opponents on those hands, I know 8 cards and have not seen 42.

Thanks,

Checkov

[jay_shark]

The probability the first card on the flop is an 8 is 2/50 . However , since there are two 8's left in the deck , you cannot simply multiply by 3 to give you the exact answer . You'll be over stating your probability since P(aubuc) = Pa+Pb+Pc -p(ab)-p(bc)-p(ac) +P(ABC) .

define A to be the prob. the first card is an 8
B is the prob that the second card is an 8 .
C is the 3rd .

P(aubuc) = 2/50*3 - [2/50c2]*3 +0
= 11.51%

ie P(AB) is the probability card 1 and 2 are 8's .

2)P(aubucudue) = 2/50*5 -[2/50c2]*5c2 +0 = 18.367%

3) You can use pokerstove to figure this out or you can do it manually . To figure it out exactly , you have to work into several cases while knowing your opponents exact hole cards . Any straight or backdoor flush can beat your kings so there are other ways your opponents can win .

An approximate probability is to take 0.8^3 = 0.512 which is the probability your kings will win against 3 opponents .The exact answer is around 54.32% according to pokerstove so you're off by a few percentage points .