Realistic Community Cards

Question

I play online poker on a few sites and recently, I have marked that I'm actually getting a series of bad beats from some awful (ly "lucky") players. My question is what are the odds of following opening in the community cards?

1. Trip flop (flops like 6K6, T9T etc.)
2. All cards above 6 in flop, turn and river (community like: 78TKQ etc)
3. All cards above 6 in community and all distinct.
4. One carder straight.
5. One carder flush.

For working out, please assume number of players on table to your convenience (if that matters). (6 would be great)

Also, please specify in the answer how you reach a specific answer (so, in future, I can compute these myself)

Answer 1

If you play a lot of hands you are going to end up seeing all kinds of "rare" events happening in poker.
Keep in mind that if a lot of players see the flop cheaply then these things will happen even more often. If you charge someone else a lot to draw cards, and they draw out on you from time to time then that's just the cost of doing business.

Anyway, a little probability can get you the odds you want, so rather than just the answers - the method so you can figure out further questions on your own

1. The chances of a pair on the flop i.e. JJ8 (let's ignore your 2 hole cards)

Take your first card C1, there's a 3/51 chance your second card C2 matches C1 or probability your second card doesn't match that is 48/51 ,
if it doesn't match C1 then the probability that C3 matches neither of the first two is 44/50 so the probability of 3 distinct cards on the flop is (48*51)*(44/50) or about 82%

So there's an 18% chance there will be a pair (or trips) on the flop.

Answer 2

Her is a partial answer, these are the odds for draw poker which is where you are dealt five cards. Source is http://probability.infarom.ro/drawpoker.html

For the flop you might look at the odds on the first three cards of Stud or Chinese poker. The only one I remember off hand is being rolled up with three of a kind the first three cards is 320:1. All the math is out three for five card hands and three card hands and fairly easy to find.

this link at the same site also has some interesting probabilities on holdem hands, might enlighten you some more

P (odds) P (percent)

one pair

0.73 : 1

42.256

two pair

20 : 1

4.753

three of a kind

47 : 1

2.112

straight

256 : 1

0.394

flush

526 : 1

0.198

full house

693 : 1

0.144

four of a kind

5000 : 1

0.024

straight flush

100000 : 1

0.001

at least one pair

1.15 : 1

53.637

at least two pair

18 : 1

5.186

at least three of a kind

42 : 1

2.352

at least three consecutive cards

0.47 : 1

32.288

at least three suited cards

0.59 : 1

37.106

Answer 3

• One question at a time

• If the site was trying to cheat they would put the pair in the hand - not the flop

• Number of players does not effect the flop

• As for working it out learn combination
  poker probability

• Community is called the board

• You don't count carder you count outs
  If you (hero) or villain need one more carder to make a straight there are 4 outs

• Be patient and the cards will come to you
  Bad beats are part of poker

Pair on the flop

combin is combination - combin is a function in Excel
combin(4,2) * 13 * 50 / combin(52,3) = 0.17647 = 18% = 4.7:1

4 to a flush

combin(13,4) * 4 * 39 / combin(52,5) = 0.05282 = 5.3% = 18:1