Sunday, July 22, 2007

NL Holdem Pre-Flop Probability - KK - Part #2

Beaten my own record for a part #2 - only a days gap! Anyhow, going to continue looking at playing Kings pre-flop in NL Holdem Poker. Summary last time was that if you hold KK there is a 77% chance of an opponent holding an Ace - going down to 49% for A-10+ and if they do hold one there is a 19% chance of an ace flopping.

Here we will look at some of the other hands people will call with and the pre-flop probability of being dealt each hand. We are then in a position to calculate your continuation bet success rate when an ace does flop... assuming that if this happens you'd be happy enough to take the pot down right there.

So, first some ranges... not all players are equal of course so we will choose an 'average' range to work with. In the earyl an online multi-table poker tournament or a cash game we are deep enough that a range of implied odds hands will generally call. We will go with, Any Pair, Any Ace with a kicker 8 or above, K-10o+ and QJo + any suited connector down to 78s. Will work it out for a single opponent first and then add other callers later.

Pre-Flop Probability of Each Hand Type:

Pairs... 6 ways of being dealt each, with only one way of being dealt KK. (12*6)+1 = 73 of the 1326 starting hands possible or 5.5%

Aces... There are 12 ways of being dealt A-8 through Q, and 6 ways of AK (you have the 2 kings of course!). Total = 66/1326 or 4.9%

Kings / Queens... There are 6 ways each of getting KQ through K10 and 12 more of getting QJ = 40/1326 = 3%

Suited Connectors... 8 ways each of getting each suited connector 78 / 89 / 910 / 10J = 32/1326 = 2.4%

This is only really any use if we turn it into a ratio - that is to say, once we are called we need to know what proportion of the time an opponent will have hand type-X pre-flop. So here it is

Pair: 34.8% of the time.
Ace: 31% of the time.
Broadway Cards: 19% of the time.
Suited Connectors: 15.2% of the time.

Well that should say something about continuation betting... after all a half-pot bet only needs to win a third of the time to break even, when an ace flops a single opponent will only hold that card 31% so into profit immediately.

Of course life at the poker tables is actually more complex than this - there are many ways an opponent could hit the flop and many hands that will call your bet regardless of whether an ace comes... imagine a ragged flop, you are in a great position to stack the guy holding QQ and a rather unfortunate position against someone holding a set of 4's!!

Calculating holdings for multiple opponents can get tricky - after all the cards held by the first guy change the probability of the second guy holding certain pre-flop hands. Will close this post by looking at continuation betting those Kings into 2 opponents when an Ace does come on the flop. We have a 31% chance of each opponent holding an Ace - so what is the combined percentage for 2? Well it is not 62%!

The way I look at it is this - there is a 31% chance the first guy has it... so we only need to be concerned with the 69% of the time he does not, now there is a 31% chance the 2nd guy has it out of the 69% - so 31% of 69% = 21% (close enough) - add that to the 31 and we are dealing with a 52% chance... still good enough but shaving some profit from our cbet success rate.

Well, hope this has given you something to think about! Will continue the theme at some point in the future with a look at probabilities of different hand combinations hitting the flop.

GL at the tables, Mark

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