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Texas Hold ‘Em - Calculating Hold ‘Em Odds
Calculating texas hold em poker oddscan help you when you make tough decisions. It could be a simple matter of getting your sums in order?
How you can use maths to get to grips with every possibility that can unfold during poker tournaments:
You might not think it’s that important to know statistics like there are 1,326 possible starting hands and 19,600
flops in Texas Hold’em, but if you don’t, you’re effectively making decisions blind and – worse still – not
maximising your chances of winning by calculating texas hold em poker odds.
One thing is certain: playing position and acting aggressively is a mathematically proven route to success. Raise
before the flop and you might steal the blinds even if you’re not holding the best hand. If you get called you’ve
got the momentum and should carry on betting because most hands miss most flops.
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But in the spirit of getting you to understand the numbers, how can this be demonstrated? With a little help from
a scientific calculator, preferably one with a ‘combinations’ (c) button), you can easily
talk yourself into getting more chips into the pot from the off (or decide that folding is actually a better
option).
For example, say you raise with a random hand in late position, and your passive opponent calls with A-K in the big
blind. What are the chances he will miss (and will therefore check and fold to your bet)? Assuming you have any two
cards below A-K, like 7-3 off-suit or 5-5, the answer is 42 c 3 (the remaining combinations of three cards below
A-K possible) divided by 48 c 3 (the total combinations possible), which is 66.37%. This means that whatever you’re
holding, you’ll win the pot two-thirds of the time through aggression alone.
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The Numbers Game
You can use the same calculating texas hold em poker odds theory to make calls on almost any situation that you might encounter playing poker. Say you’re
in a tournament and you’re short-stacked. You’ve got less than ten big blinds left, so you decide that on the next
decent hand you’re going to make an all-in move while you’ve still got enough chips to push people off the pot and
make drawing hands pay to stay.
Here your decisions are determined pretty easily by a few calculations. Say you’ve got an Ace with a weak kicker – a
Five for example. Now you might automatically assume that any Ace is a stick-on favourite, but is this correct?
Let’s start with you in the small blind when everyone’s folded round to you. You have 9500 chips and the blinds are
500-1000. Once you’ve put in your small blind of 500 you have 9000 left and can win 1500 by moving all-in – this
means you’re getting odds of 1/6 on your money. Which isn’t great on the face of it. To make it a worthwhile move
you should be looking at being at least that big a favourite to take the pot down.
There are 1225 potential hands that the big blind could have, but how many will he call with that are beating your
A-5? This, of course, depends on many factors: stack sizes, what sort of player he is and so on. But for argument’s
sake, let’s imagine the big blind is a tight player who will call with any pair Sevens and up, and A-8 through to
A-K. There are six combinations for each pair (4 c 2) except A-A – there are only three (3 c 2) as you hold an Ace –
and 12 combinations for each A-X hand (three Aces combined with four Kings, Queens, Jacks and so on). In total,
then, there are 117 combinations beating you, or less than 10% of the hands he can be dealt, making moving in a
profitable play.
What Are The Chances?
Now what if you were on the button with 9000 chips and two other players left? Well, assuming all the details are
the same, each of the two players will call with 117 out of the remaining 1,225 (9.55%) combinations and fold the
other 1,108 (90.45%) hands. And by multiplying together the chance of each of them folding (90.45 x 90.45 / 100) you
get the chance that both will fold (81.8%). This means you’ll win the blinds about nine hands out of 11, which
isn’t ideal when you’re only getting about 1/6 on your money. But you have to factor in the chance that if called
you can double or even treble through holding the worst hand.
Underdog
A quick visit to an online odds calculator reveals that against a bigger Ace you’re about a 3/1 dog and against
pairs lower than Aces you’re about a 7/3 dog. For the sake of simplicity and because you’re more or less screwed if
both players call or one finds Aces, let’s round these numbers up and say that when called you’re always a 3/1 dog.
Now you can say that nine times out of 11 you will win the blinds (1500 chips) and two times out of 11 you will
lose 75% of the time (a loss of 9000) and win 25% of the time (an average of 9750 depending on which stack calls). So
when called your net result is 9750 x 0.25 - 9000 x 0.75 = -4312.25.
Now, to see whether this is a profitable play or not, the odds need to be factored in. Going on the information
you have you’ll win 1500 nine times and lose 4312.25 twice. So the net result on the play each time you make it is
1500 x 9 - 4312.25 x 2 / 11, which is 443.22, making it a profitable play, but not by much. In fact you might want
to think again before putting all your chips on the line. The moral of the story, then, is that an Ace with a small
kicker isn’t as good a hand as it might appear for making your stand.
And now you understand the reasons why, you can apply the calculating texas hold em poker odds numbers to your overall game. Admittedly, we’ve used
one very specific example here, but the general concepts can be used in any given situation. And now the winter
nights are drawing in, what better way to while away the long, dark hours?
However, we don’t want to scare you off poker because of some scientific calculating texas hold em poker odds ponderings. As you know by now, poker
is fun and we’re not suggesting you should turn it into an academic study. Play the game as you feel it and not
strictly by the numbers. The maths just makes poker that bit more transparent, which if you can master, will give
you the edge when you’re up against some tough players. And no one can dispute that poker is more fun when you’re
winning.
Play Poker.
Texas Hold 'Em Poker explained.
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Calculating Poker Odds.
Play Online Poker For Fun.
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