Missed AK odds at the river

[Pyroxene]

I am sure most of you have been there. You're dealt AK and you raise, only to be called by the calling station. The flop misses you and you pound away but he keeps calling. Finally, at the river you have missed completely. But, at the same time, the caller is a known idiot that has called to the river with nothing before. He may flip to show flopped trips, he may flip to show 94s that completely missed everything from the get go.

Or you are at the home game and the local 'pro' decides to play blind against your AK in the same situation. You know you missed and he could have absolultely anything.

Where do you stand?

Here are the odds for a missed AK against a random hand:

UNPAIRED BOARDS

When the board has no pairs, no straights, no flushes.
Example: :Jh:

1.6:1

When the board has no pairs, one possible straight using two cards, no flushes.
Example: :Jh:

1.7:1

When the board has no pairs, two possible straights each using two cards, no flushes.
Example: :Jh:

1.9:1

When the board has no pairs, one possible straight using one card, no flushes.
Example: :Jh:

2.7:1

When the board has no pairs, two possible straights each using only one card, no flushes.
Example

4.0:1

When the board has no pairs, no straights, and 3 to a flush that is not the suit of either of your cards.
Example: :Jh:

1.8:1

When the board has no pairs, no straights, and 4 to a flush that is not the suit of either of your cards.
Example: :Jh:

3.7:1

When the board has no pairs, one possible straight using two cards, and 3 to a flush that is not the suit of either of your cards.
Example: :Jh:

1.8:1

When the board has no pairs, one possible straight using one card, and 3 to a flush that is not the suit of either of your cards.
Example: :Jh:

2.7:1

When the board has no pairs, two possible straights each using only one card, and 3 to a flush that is not the suit of either of your cards.
Example

4.4:1

When the board has no pairs, one possible straight using two cards, and 4 to a flush that is not the suit of either of your cards.
Example: :Tc: :Jh:

3.9:1

When the board has no pairs, one possible straight using one card, and 4 to a flush that is not the suit of either of your cards.
Example: :Jh:

5.5:1

When the board has no pairs, two possible straights each using one card, and 4 to a flush that is not the suit of either of your cards.
Example: :Jh:

8.5:1

PAIRED BOARDS

When the board has one pair, no straights, no flushes.
Example: :Jh:

0.95:1 (51% chance of winning)

When the board has one pair, one possible straight using two cards, no flushes.
Example: :Jh:

1:1

When the board has one pair, one possible straight using one card, no flushes.
Example:

1.5:1

When the board has one pair, one possible straight using two cards, and 3 to a flush that is not the suit of either of your cards.
Example:

1.2:1

When the board has one pair, one possible straight using one card, and 3 to a flush that is not the suit of either of your cards.
Example:

1.7:1

When the board has one pair, one possible straight using two cards, and 4 to a flush that is not the suit of either of your cards.
Example:

2.7:1

When the board has one pair, one possible straight using one card, and 4 to a flush that is not the suit of either of your cards.
Example:

3.7:1

TWO PAIR BOARDS

When the board has two pairs, and the 5th card is lower than the lowest pair.
Example: :Td: :Tc:

0.43:1 (70% chance of winning)

When the board has two pairs, and the 5th card is higher than the highest pair or inbetween the two pairs.
Example 1: :Td: :Tc: :Jh:
Example 2: :Td: :Tc:

0.64:1 (61% chance of winning)

TRIPPED BOARDS

When the board has trips, no straights, no flushes.
Example: :Tc:

0.53:1 (65% chance of winning)

When the board has trips, one possible straight using two cards, no flushes.
Example: :Th:

0.61:1 (62% chance of winning)

When the board has trips, no straights, and 3 to a flush that is not the suit of either of your cards.
Example: :Jc:

0.65:1 (60% chance of winning)

When the board has trips, one possible straight using two cards, and 3 to a flush that is not the suit of either of your cards.
Example: :Tc:

0.69:1 (59% chance of winning)

WHAT TO TAKE AWAY FROM THIS.

A missed AK is actually a favorite against a random on a paired board with no other possibilities and a pretty big favorite on a two pair board when the 5th card is lower than the lowest pair.

Toss in the cards when there are 4 to a flush and when there are two one card straights on the board. At that point there are just too many single cards that the opponent can hold and have you beat.

[a500lbgorilla]

Yes, but the random hands you're betting will probably fold to any bet you make. So an unimproved AK is nothing but a small pot winner.

-'rilla

[ekillian]

You can't think like this and expect to win. In the long run you are not a favorite against a player who has called you every street.

[Pyroxene]

You can't think like this and expect to win. In the long run you are not a favorite against a player who has called you every street.

The list is no more than what I billed it as, odds against the random hand. I was inspired by watching a fish do the call thing last night with any hand, even calling final bets when he had nothing and calling final bets when he had the nut straight. Then I recalled the story of the poker pro playing blind against opponents.

Obviously, if a normal player calls to the river they do not have any old random hand. They have something and your AK is most likely worthless.

[johnnyawe]

Thanks for the chart. I've often wondered about this. I guess the moral of the story is that for all the possibe boards you came up with, there was only one where the odds are in your favor vs. a random hand.

[PokerPatNEU]

Thanks for the chart. I've often wondered about this. I guess the moral of the story is that for all the possibe boards you came up with, there was only one where the odds are in your favor vs. a random hand.

I coun't a couple more than 1

[wobbler]

Yes, I count 7 boards where AK is the favorite against a random hand. But even a calling station has SOME discrimination of hands he will call with, so I'm not sure AK would really be a favorite.