The value of having an Ace when pushing

[John Hurst]

I like to think about poker at work. I like numbers.
So here is a question I tried to solve today:
If you have an ace in your hand and know an opponents range of calling hands how much less likely is it for your opponent to call an all-in given that there is 1 less Ace in the deck?

I just assumed a range of calling hands for a fairly tight player and ran some numbers.

Here it is:

Hand # of combinations w/4 Aces # of combos w/3
A10 32 24
AJ 32 24
AQ 32 24
AK 32 24
99 12 12
1010 12 12
JJ 12 12
QQ 12 12
KK 12 12
AA 12 6
Total: 232 186
Call % 9.5% 7.6%

So if you have an Ace in your hand you are getting called 2 fewer times per 100 pushes.

I found this pretty interesting and hopefully somebody else latches unto the concept and does some more useful work.

[curtains]

Yeah having an ace is underrated IMO. People are too scared to be dominated, but dont realize that they sometimes get called by worse hands, and also it will be less likely that you are called solely because you have an ace.

The problem is that it's hard to forget all those times you push with A3o on the button and get called by A8s. They leave a lasting memory that make people want to start folding aces and instead raise with non dominated hands like T7s and so on.

[Bill Poker]

[ QUOTE ]
I like to think about poker at work. I like numbers.
So here is a question I tried to solve today:
If you have an ace in your hand and know an opponents range of calling hands how much less likely is it for your opponent to call an all-in given that there is 1 less Ace in the deck?

I just assumed a range of calling hands for a fairly tight player and ran some numbers.

Here it is:

Hand # of combinations w/4 Aces # of combos w/3
A10 32 24
AJ 32 24
AQ 32 24
AK 32 24
99 12 12
1010 12 12
JJ 12 12
QQ 12 12
KK 12 12
AA 12 6
Total: 232 186
Call % 9.5% 7.6%

186/232 = 80% So if you have an Ace in your hand you are getting called 20 fewer times per 100 pushes.

I found this pretty interesting and hopefully somebody else latches unto the concept and does some more useful work.

[/ QUOTE ]

isnt it 2 fewer times per 100 pushes? 9.5%-7.6%=1.9%

[John Hurst]

[ QUOTE ]
isnt it 2 fewer times per 100 pushes? 9.5%-7.6%=1.9%

[/ QUOTE ]
Good catch. Thank you. Got ahead of myself.

[curtains]

Most of the time that you push with ace high, your opponents calling range will be much looser than that. You should be pushing with any 2 in a lot of spots if your opponent is calling with 7% of hands.