My questions involve, if I open with an Ace hand, how often will a caller also have an ace, the flop have an ace, or both?

I use the following opening requirements in early position, opening:
22+, A2+, KJ+, QJ+, 76+ AQo+, which leaves me opening 14% of hands (182/1326). Of these 78 or 41% have at least one Ace.

If hypothetically a caller has the same calling requirements as my openers, that would remove 21 aces and the caller would be left with 57 Aces out of 161 hands or 35% of his hands.

If I don't have an Ace but one flops, I believe the above math would still hold, and each caller would have about 35% chance to have an Ace.

If both the flop and I have an ace, this would remove 20 additional aces, and a caller would have 37 out of 141 hands or about 26% chance to also have an ace.

If this math is approximately correct, then two thoughts emerge:
1. If a flop contains an Ace but I don't, this is a reasonable bluffing opportunity, as a caller will only have 35% chance of having one.
2. If both the flop and myself have an ace, a caller only has 25% chance of also having one, so this makes checking the flop a very reasonable play.

Would love to hear comments on both the math and the resulting plays. Also, if you can give a reference for the actual math of the above, I would love to see it.

Your opening requirements are very loose for 9/10 handed games. A calling range shouldn't have that many weak aces in it from any position. Your math doesn't work with multiple opponents because of card removal.

For your general thoughts:
1. Opponents will expect you to c-bet ace high flops and will call more often no matter what they do have. You should still c-bet some of them but the percentage should be a bit lower.

2. Your play becomes too obvious even for low stakes if you bet when you don't have an ace and check when you do. In most situations you make your money when you are taking the lead on betting so you should be betting your made hands.

Also, this is ignoring the actual board texture and is assuming your facing one opponent. Board texture is a big topic itself but multiple opponents is easy. No matter what the board looks like your rate of bluffing should go down fast for each additional opponent.

This is what flopzilla is for

Your math is correct. In theory I believe you check fairly frequently to an IP cold caller, but in practice cold calling ranges are very weak and you have a large advantage on A-high flops. You should get enough folds to profit from fold equity alone because the opponent doesn't have a strong enough range to continue very frequently. Also since you obviously can never have overcards, you don't have many air hands that have much equity as checks. If you check KQ and the turn is a K, you're still not too happy about facing action. It depends on specifics but I often c-bet air heads up on A-high flops vs. weak opponents, especially if they're not extremely passive like the population since aggression reduces check EV of weak hands. Multiway I will still often c-bet air but I usually want some sort of equity, like double backdoor draws or a gutter, etc.

Also remember that you can delay c-bet, so checking isn't necessarily giving up and you might want to delay c-bet in some situations instead of 100% c-bet, even if you can do the latter profitably.

Kind of hard to give any better advice without specifics. Generally yes, I'm c-betting when I don't have an Ace, but I'm also generally c-betting when I do vs. passive opponents since they won't likely give me any value by bluffing vs. my check.

[QUOTE=QuadJ;56610790]Your opening requirements are very loose for 9/10 handed games. A calling range shouldn't have that many weak aces in it from any position.

I am basically using the opening/calling requirements of Jonathan Little combined with Ed Miller in The Course. Miller addresses calling with weaker aces by classifying the opener as strong or weak/loose, with the differentiation being a strong opener is someone who will also open by limping, thus when he opens by raising, he is likely stronger than someone who always opens with a raise. For strong openers, Miller advocates discarding suited aces below ATs when calling. I generally follow this, as well as backing off if I know the original opener is seriously tight.