Let’s take a close look at what happens when cards are removed, that is, not available anymore, for whatever reason.
Reasons:
1) It is in your hand
2) It appears on the board
3) It is in an opponent’s hand
The last reason is only valid for games like seven card stud, where you get to see some of the opponents’ cards. Or, of course, in holdem if a card is inadvertently displayed by one of the players, or the dealer, which is not unheard of.
Adjusting Calculations:
As the cards become revealed during the hand, it is important to constantly update your calculation – your hand’s chances in the pot.
Every action at the table causes you to reevaluate your picture of the opponent’s likely holdings. This is an acquired skill.
Before you can start using your intuition and experience, you need to consider the facts that they are based on.
As the cards become revealed, the likelihoods of your opponent’s possible holdings change.
Removal for Pairs:
The number of combos for pair hands is six. When cards are removed, logically, the number of combinations goes down rapidly.
Card Removals for Non-Pairs:
Non-pairs come in 16 variations in an untouched deck. As the cards are removed, the number of combos goes down. But the exact numbers depend on which cards are missing.
For example: AK comes in 16 combinations and if one ace is removed, 12 combinations are remaining. But when a second card is removed, the remaining combos depend on if it’s a second ace or an ace and a king combo. If two aces are gone, then eight combos remain. If it’s an ace and a king, there are nine combos left.
When three cards are removed, there are either six or four combos left. With three cards gone, there can be four, three or zero combos left. The number is zero, if all four aces or all four kings are gone. And so on and so forth.
Examples:
Here are a few examples of how you can use the numbers above. We’ve shown the average or approximate number, and provide the exact number in parentheses.
You have Ace/King. The number of Ace/King for the opponent is nine.
You have Ace/Ace. The number of Ace/King for the opponent is nine (or actually eight).
You have Ace/King. The number of Ace/Ace for the opponent is three.
You have Ace/Ace. The number of Ace/Ace for the opponent is one.
You have Ace/King, there is an Ace on board. The number of Ace/King for the opponent is five (or actually six).
You have Ace/King, there’s an Ace on board. The number of Ace/Ace for the opponent is one.
You have Ace/Ace, there is an Ace on board. The number of Ace/King for the opponent is five (or actually four).
You have Ace/Ace, there is an Ace on board. The number of Ace/Ace for the opponent is zero.
Summing ‘em Up:
As always, you need to sum up all of the numbers and combine them with your hand’s chances against all of the possible hands that your opponent could possibly be holding.
