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DRAW POKER STRATEGY

When it comes to Poker strategy, there are a few things to get straight right off the top. You could call these the Golden Rules of Poker 'cause they apply to pretty much any Poker game you're likely to play:
  • Don't play cash poor: as a general rule you should start with 40-50 times the table limit.
  • If you've got nothing in your hand, get out.
  • If you've got a cinch hand, make them pay to see it.
  • If they've got you beat, fold.
  • The goal is to beat the other players, not have the highest hand. If everyone else folds, you take the pot.
  • Don't try to beat a better player: if you're lucky, you'll win small; if you're not, you'll lose big.
  • There's an even chance that you won't better your opening hand.
When it comes to Draw Poker Strategy we begin by considering the rank of the winning hands. In the Rules of Draw Poker, we introduced the 5-card hands and their ranking. Here's some idea of the odds on receiving those hands on the opening deal:

Chances of being dealt
in the original 5 cards
Royal Flush 1 in 650,000
Straight Flush 1 in 72,200
Four of a Kind 1 in 4,200
Full House 1 in 700
Flush 1 in 510
Straight 1 in 250
Three of a Kind 1 in 48
Two Pair 1 in 21
One Pair 1 in 2.4
No Pair 1 in 2

Based on these chances of receiving an opening hand, there are a few things you can immediately conclude:
  • the more players at the table, the greater the chance that one or more players has a Pair, for example. In other words...
  • the more players at the table, the lower the relative value of the lesser ranked hands.
  • if you haven't got a Pair or better, or four cards to a Flush or Straight, Fold immediately.
Perhaps this last bit of advice needs some elaboration. What it comes down to is this: if you hold nothing in the opener your chances of improving and beating the other players are too slim. Of course this means that you'll fold most of your opening hands. Welcome to Draw Poker.
So let's assume you've got a little something to build on. Every beginning player wants to know whether they should hold a kicker and a Pair, or just the Pair. Same with Trips. As you'll see in the following, the odds almost always favor tossing the kicker:

Chances of making:
Any improvement Two Pair Three of a Kind Full House Four of a Kind
Drawing three cards to a Pair 1 in 2.5 1 in 5 1 in 8 1 in 97 1 in 360
Drawing two to a Pair with kicker 1 in 3 1 in 5 1 in 12 1 in 120 1 in 1100
Drawing two to Three of a Kind 1 in 8.5 -- -- 1 in 15.5 1 in 22.5
Drawing one to Three of a Kind with kicker 1 in 11 -- -- 1 in 15 1 in 46

Needless to say, the better your opener, the better your chances of improving it. But forget about trying to build something out of a three card Flush or Straight: your odds are 1 in 23 and 1 in 150 respectively. It's highly unlikely that the pot would ever justify that kind of risk.

On the upside, observe the following chances if you hold four cards to build on:
When drawing one card to:
Four cards of a Flush
1 in 4.5
Straight open at both ends
1 in 5
Straight open at one end
1 in 11
Straight open on the inside
1 in 11
Straight Flush open at both ends
1 in 23
Straight Flush open at one end
1 in 46
Straight Flush open on the inside
1 in 46