To start with you get 5 cards.
Your initial hands will be distributed as follows:

Starting hand Distribution:

• 50.1% High Card
• 42.2% Pair
• 4.8% Two Pair
• 2.1% Three of a Kind
• 0.4% Straight
• 0.2% Flush
• 0.1% Full House
• 0.02% Four of a kind
• 0.002% Straight Flush

Important points to take away from this:

1. Just over half the time you will not even have a pair in your hand to start with. But the same applies to your opponent of course.
2. Roughly 2 times out 5 you'll have a pair
3. You only get two pair once every 20 deals or so - you have a good starting hand, but it's not likely to improve - be wary.
4. About once in every 50 deals or so you'll start with three of a kind - this is a powerful hand and is likely to win at showdown. Try not to scare your opponent away, but also try and make sure you get chips in the pot to capitalise on your good fortune.
5. Hitting a pat straight,flush or better is very rare - and as you'll not be drawing any cards your opponent should realise you have a good hand after the draw. Same as for three of a kind, try and maximise your gain without scaring your opponent away.

Drawing Probabilities:

Drawing one card to an open-ended straight flush (e.g. 6789 all clubs).	32% (~ 1 in 3) you'll hit a straight or better.
Drawing one card to an inside straight flush (e.g. 5679 all clubs).	26% (~ 1 in 4) you'll hit a straight or better.
Drawing one card to a flush.	19% (~ 1 in 5) you'll hit.
Drawing one card to an open ended straight.	17% (~ 1 in 6) you'll hit.
Drawing one card to an inside straight, or to two pair, or three of a kind when you keep a kicker.	9% (~ 1 in 11) you'll hit.
Drawing two cards to three of a kind.	10% (~ 1 in 10) you'll improve.
Drawing two cards to a pair+kicker (e.g keeping 66A).	17% (~ 1 in 6) you'll hit two pair, and about 9% (~ 1 in 11) you'll make trips or better.
Drawing two cards to a three-flush or three straight.	Roughly 4% (~ 1 in 24) you'll make it.
Drawing three cards to a pair.	16% (~ 1 in 6) you'll hit two pair, 11% (about 1 in 9) you'll hit trips, and about 1% (1 in 100) you'll hit a full house or four of a kind.

How to Draw.

When you draw you have limited information. In short all you have is the way the betting went pre-draw, and possibly you know how many cards your opponent has drawn.

Some of my thoughts on particular situations:

• Assuming that your opponent is not a fool is generally the best policy.
  • If there was no raising pre-draw and your opponent takes 1, they are likely trying to fill a straight or flush. Probably they won't make it, so you should try and draw to give yourself a high pair or better.
  • If however there has been raising it is more likely that they have two pair. Again, you can take a reasonable guess as to what hand they have, and what their chances to improve are, and hence what you will need to get to beat them.
• Generally it is best to draw in the manner which gives you the best chance of improving. Deception overpracticed stops being deception.
• If you think by the betting style of your opponent that they have a pair of aces, or two pair then it might be a good idea to draw one to your trips, trying to make them think you are drawing to a straight or flush.
• If the pot wasn't raised and you have garbage, don't be afraid to change all your cards, or all but one.
• In my opinion, depending on the way the betting round has gone, it is often better to keep two high cards and draw three to those instead of drawing to a lower three-straight or three flush. Your opponent will be wary that you already have a pair, and as you'll see from above it's more likely than not that they do not themselves have a high pair so if you hit one you are more likely to end up with a winning hand than you would with a busted flush or straight draw

After the draw.

Well, this is judgment time.

You need to balance how the betting went pre-draw, how many cards your opponent has changed, and any action (bet/check) they make after the draw.
Once you have an idea of how your opponent plays this should become easier. review, review, review.

Remember, the aim is to end up with all the chips at the end of the game. Not to try and win every pot.

If you didn't make a hand that you think will beat your opponent there is no shame in folding and getting 5 brand new cards...this time you may get that Royal Flush you were after..of course if you made a crying call and threw all your chips away you didn't get these new cards.

Given the choice between slim chance and no chance, I'll take slim every time, and recall the old maxim "All it takes is a chip and a chair."

Hopefully the maths above, and my random thoughts make sense - feel free to drop me a line with any questions and I'll happily discuss odds etc. Or pop along to The Chip and a Chair Club