What's the chance they have an Ace?

You raise preflop without an Ace and get called. An Ace flops. What's the chance they have an Ace? What's the chance a player calls a preflop raise with an Ace in their hand? How do different general types of players compare in their chances of having it in this situation?

The main thing I'm looking for is the average Fold Equity (FE) and whether it's really worth it to continuation bet generally. I know it's conventional wisdom but there's no reason why we can't reexamine it.

If an Ace shows up on the Flop, then the chance of any given player getting dealt an Ace preflop is 3/50+3/49=~12.12% (right?)

The hands that Loose players call preflop raises with generally: AA-22, AKo-A2o, AKs-A2s, KQs-KTs, KQo-KTo, QJs-Q9s, QJo-Q9o, JTs-J9s, JTo-J9o, suited connectors T9-54, unsuited connectors T9-65, gap suited connectors T8-64, gap unsuited connectors T8-64--- total chance of being called preflop if there's an Ace on the Flop: 35% (I admit it may be too high, but for some people it may even be higher) On second thought, I'll lower it to about 31% because very few people won't reraise with AA-QQ, AK)

Chance of them having an Ace after calling preflop raise: ~37%; chance of any given player calling/raising Flop continuation bet without at least Top Pair after calling preflop: ~33% with some sort of Pair, ~11% with some sort of Draw, ~10% pure bluff...total % of Flop continuation bets being called/raised by any given player= ~91% (!)

That means FE against Loose players is (predictably) very low and a continuation bet against them is usually not a good idea.

Now for Tight players: AA-22, AKo-AQo, AKs-AQs, KQs-KJs, QJs-QTs, JTs-J9s, suited connectors T9-54--- total chance of being dealt preflop: ~12.3%, or ~10% without AA-QQ, AK

Chance of having an Ace: ~10%; chance of any given player calling/raising Flop continuation bet without at least Top Pair after calling preflop: ~5%, ~11% with some sort of Draw, ~10% pure bluff...total % of Flop continuation bet being called/raised by any given player= ~36%

So continuation bets are very effective against these players.

But what if you don't have any Reads? Let's take the average between the Loose and Tight player to get an idea of the average FE.

36+91=127/2=63%

This means that if you bluff an unknown player you would need to bet about 2/3 the pot every time to break even. So if you're the type to bet Full Pot when you bet, whether bluffing or with a hand, you SHOULD NOT continuation bet against an unknown opponent. On the other hand if you're the type to bet Half Pot, then a continuation bet is A GOOD MOVE. I'll leave whether it's good to only bet Half Pot when you're trying to protect the pot for another day...

Oh, and everything changes when you're not Heads Up against one opponent. Then continuation bets become less and less EV.

PS: Anyone who points out something crucial I forgot gets E-cool points...

What limits?

at the low limits, you can almost count on an ace

Thoes players think that A3s is nuts on an ace high rainbow flop.

Originally Posted by Iconoclastic

If an Ace shows up on the Flop, then the chance of any given player getting dealt an Ace preflop is 3/50+3/49=~12.12% (right?)

Not quite. you can see 5 cards with one Ace. Odds are 1 - (odds of missing an A with both hole cards) ie) 1 - (44/47*43/46) = 12.5%.

Now going to extremes and assume that no-one will fold an A at a full table you have 1 - (odds of all 18 hole cards missing) = 77.46%

Now going to extremes and assume that no-one will fold an A at a full table

In other words at the low limits =)

100 %

Isnt this a case of 'what cards does my opponent think i have?'
Therefore, why would you raise without an ace and then attack an ace high flop with a nice big bet?

I havent got the hand history but i did it in the last gauntlet tourney.
I raised both for the first time in 4 orbits and from position then pushed all in on an ace high flop with K4, basically saying that no matter if you had the ace so did i with a great kicker. I got called by AQ (it was a good call imo, i just thought i wouldnt happen!)
The same applies here surely. Unless you know your up against a calling station then bet out as if you have what is there to see. They either raise you back to test or they have you beat anyway and just want you to pump money at them eg set.
If i have KK get a caller and get an ace high flop i will still atatck the pot 100%. Its about what he doesnt have and what he thinks you have imo.

Definitely a "What does my opp think i have?" You could easily be the big shot with Aces + Strong kicker. Maybe he's playing this hand with suited connectors? KQ? Small pockets? You always have to continuation bet against 1 opp, for information and fold equity. If its A x x rainbow,a nd you're holding KK, how does he know you didnt just pair your aces while holdign AK? Unless he made trips or picked up a draw, or he is the guy holding AK, you are taking down the pot. If he has a hand, you will find out by the way he plays after your continuation bet (raise/call). Calculating the actual odds he was dealt an ace and didn't fold it doesn't really come into play as much as hid response to how you bet the flop when an ace falls on it.

Regarding KK and A-high flop:

If you get called and the turn doesn't give you a set can you do anything other than go into check/fold mode? It seems to me even the worst players are not going to call a preflop raise then a bet on an A-high flop without having an ace or a set.