Playing With Starting Hand Frequencies
Here's another thing I get asked about from time to time, so I'll make this thread and bookmark it so I can just link people instead of having to explain it over and over. This post has to do with ways to build randomness into your play by using the suits of the cards you're dealt as your randomizing agent.
Pocket Pairs
There are 6 ways to be dealt a pocket pair. Taking pocket Aces as an example, there is:
1. A:s: A:c:
2. A:s: A:h:
3. A:s: A:d:
4. A:c: A:h:
5. A:c: A:d:
6. A:h: A:d:
(1/6) 16.667% - Pick one particular combination of suits, i.e.: two black cards.
(1/3) 33.333% - Pick two particular combinations of suits, i.e.: two black cards and two red cards.
(1/2) 50.000% - Pick one suit, i.e.: any combination of suits with a spade.
(2/3) 66.666% - Pick two suits, and play them if only one of them is in the hand, i.e.: play the hand if it has one heart or one spade, but not if it has a heart and a spade.
(5/6) 83.333% - Pick one particular combination of suits and don't play it, i.e.: don't play two red cards.
Suited Non-Pairs
There are four ways to have the suited version of a particular hand because there are only four suits.
(1/4) 25.000% - Pick one suit to play, i.e.: only spades.
(1/2) 50.000% - Pick one color to play, i.e.: only red cards.
(3/4) 75.000% - Pick one suit not to play, i.e.: you play all suits but spades.
General Non-Pairs
If you take any non-pair hand, AK for example, there will be 16 different combinations of suits possible because there are 4 possible suits for the Ace, 4 possible suits for the King, and 4 * 4 = 16. These aren't particularly useful but I'm going to include half of them for completeness so that I won't get asked about them when I link people to this post which would defeat the purpose of typing this out in the first place. So here we go on the most boring thing I've ever bothered to type out.
(1/16) 6.250% - Pick one suited combination to play, i.e.: both cards are spades.
(1/8) 12.500% - Pick two suits and play the offsuit versions with those two suits, i.e.: both combinations of one spade and one heart.
(3/16) 18.750% - Pick one suit, and play the hand when the higher of the two cards is that suit, and the hand is not suited, i.e.: pick spades and play AK as long as the Ace is a spade and the King is not.
(1/4) 25.000% - Pick one suit, and play the hand when the higher of the two cards is that suit, i.e.: pick hearts and play AK as long as the A is a heart.
(5/16) 31.250% - Pick one black suit, and play the hand when the higher of the two cards is that suit, and also pick one red suit, and play the hand when the cards are suited of that red suit, i.e.: pick spades and hearts, play any AK hand where the A is spades or the hand is AKs of hearts.
(3/8) 37.500% - Pick two suits, and play the hand when the higher of the two cards is either of those suits, AND the hand is not suited, i.e.: pick spades and clubs and play AK if the Ace is a spade or club, but don't play if it's AKs of spades or clubs.
(7/16) 43.750% - Pick a suit, and play the hand as long as either card of the hand is that suit, except when they are both that suit, i.e.: pick spades and play any AK that has the Ace of spades or King of spades, but not AKs of spades.
(1/2) 50.000% - Pick a color red or black, and play the hand as long as the higher of the two cards is that color, i.e.: pick black and play any AK with a black Ace.
For the other possible frequencies for unpaired hands just reverse the process, i.e.:
(15/16) 93.750% - Pick one suited combination not to play, i.e.: Play all combinations of AK except AKs of spades.
