poker heads up odds

i am trying to figure the odds of an event happening in Texas Hold Em Poker.?

I want to know in Texas Hold'em Poker, what is the odds of a hand of 4 of a kind being beaten by either a higher 4 of a kind or a straight flush.

Here's how I would approach this problem:

First, you have a four of a kind. One of three things happened:
1. The community cards hold a four of a kind
2. The community cards hold a 3 of a kind and you hold the fourth card
3. The community cards hold a pair and you hold the other pair

In the case of #1, nothing interesting can happen. It is impossible for another person to beat the four of a kind on the board, so this is uninteresting.

In the case of #2, there are four remaining cards - the other two community cards and your opponent's two cards. So the following is possible:
2A. These four cards create a higher four of a kind that yours.
2B. These remaining four cards can be combined with one of the three of a kind to create a straight flush.

In the case of #3, there are five remaining cards - the three other community cards and your opponent's two cards. In this case we get the following possibilities:
3A. These five cards contain a four of a kind that beats your four of a kind.
3B. These five cards form a straight flush.
3C. Four of these five cards combine with one of the showing pair of community cards to create a straight flush.

Now, these are the only ways you can get beat. This is a complicated question, and so I'm assuming you have some ability to calculate probabilities already. The key is to calulate the probability of each event above happening and combining them together:
P(2)*[P(2A)+P(2B)]+P(3)*[P(3A)+P(3B)+P(3C)]

Note: The above is the probability of this event happening. You might also be interested in the conditional probability of you getting beat give that you alreay have your four of a kind. In that case, you just exclude the P(2) and P(3), to get
P(2A)+P(2B)+P(3A)+P(3B)+P(3C)

I didn't actually find the answer, but I'm sure it is VERY small!

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Preflop Strategies And Odds Calculations - The Key To Winning Big

Before we get into your poker preflop strategy, it might help to know what a “preflop” is. Essentially, the term preflop refers to the original hand you’re dealt before the flop.

When you look at the hand you’re dealt, there are certain things to look for to help your preflop poker strategy. Remember: even if you hold high aces or double kings or queens, you do not want anyone to know. Why? Because the other players will fold faster than a Laundromat worker on dry cleaning day.

But what are you looking for in the ideal preflop hand? Remember that in poker you’re given five cards. The ones you feel are your best, you keep with you; the others you lay down to receive your flop.
The best cards, naturally, are the high cards: Ace, King, Queen, Jack, etc. So, when you’re given the initial deal, if your preflop looks like this, you should keep your poker face, but grin big inwardly. The best preflops are listed in descending order. (The cards are listed by the first letter of the card):

•    AA, KK, QQ, JJ, AK
•    TT, AQ, AJ, KQ, AK
•    99, JT, QJ, KJ, AT, AQ
•    T9, KQ, 88, QT, 98, J9. AJ, KT
•    77, 87, Q9, T8, KJ, QJ, JT, 76, 97
•    66, AT, 55, 86, KT, QT, 54, K9, J8, 75
•    44, J9, 64, T9, 53, 33, 98, 43, 22, T7, Q8
•    87, A9, Q9, 76,42, 96, 85, J8, J7, 65, J8, J7, 65, 54, 74, K9, T8

Okay, you have your preflop, now what? The next step is to use a poker odds calculator to calculate your odds. There are online calculators that do the work for you. However, there is a way to do the math in your head.

Naturally, the odds are in your favor if you’re playing with players who are less skilled than you. But if you’re playing with better hands, then you’ll need to know how to figure out your odds.

There are thirteen cards in each suite. Look at your hand: you have a 10h, Jh, 10d, 2h, 4s. What now? Look closer; there are thirteen hearts in a deck and you have three, so there are ten more left.

Now it’s time to use your mental poker odds calculator. Take the number of hearts you have (3) times the number left in the deck (10). The result is 30 – or 30%; you have a 30% chance of getting a flush. You also have two 10s.

When you take the number of 10s you have and figure out the number you need for to have 4-of-a-kind, you can see that it’s 50%. The same is said for a straight. You have a 30% chance of getting a straight; the same percentage for a straight-flush.

It’s all a matter of basic math to calculate your odds. Check the statistics and calculate carefully. When you figure it out, you’ll be able to work the equation into your preflop success.

About the Author

If you’re looking for ways to calculate your odds, check out Casinator.com. They have an excellent online odds calculator. Doing the calculations in your head will get a percentage close to the actual odds. But if you want an exact calculation, check out the Casinator.com calculator for results that are precise and accurate.