Visible Aces vs. any two cards

[apfel]

op said unlimited stacks.

[Nichlemn]

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it does not make sense to raise with the aces preflop.the potsize preflop is not important for the aces.i dont know if the random cards should raise preflop.(pocket pairs,red suited connectors)

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Hmm, I was going to say that it mattered whether Aces raised preflop by getting in more value when they're guaranteed to be ahead, but with effectively infinite stack sizes, I don't think the implied odds change at all (Aces win a 3x larger pot when the random cards give up, but the random cards also win a 3x larger pot anyway). I suppose that makes Aces indifferent to raising.

I could see some merit for hands with better implied odds raising, making the random card player play bigger pots when they have a better shot of winning. However, I think this could remove a crucial advantage of the random cards having a disguised hand: e.g. scary boards are harder to play at them if you've limped and always raise suited connectors.

[jogsxyz]

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That's not necessarily true. Look at the toy game in MOP 19.3. Only the clairvoyant is dealt a card. Standard deck. Ace or king, Clare(clairvoyant) wins, else the defender wins. Clare is dealt 2/13(or ~ 15.385%) winners. Both players ante 5 units. Three streets of pot size bets(my own restriction).

Since the defender cannot profit by betting, only Clare may bet each street. Defender may call or fold. Clare is the favorite in this toy game, even though she is dealt only 15.385% winners.

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my bad aaron, missed that part

@jog: why are you assuming that AA will not call down?

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Defender with AA is assumed to defend optimally.
This means on each street call pot/(pot+bet) of
the time. Half the time against pot size bets.

But the one card game is not the same as this AA
game. Know of no utility which tells any two cards'
equity after flop. That is how often it will be ahead
of the AA after the flop.

jogs

[jogsxyz]

The AA game.
The clairvoyant needs to bet so that she
is indifferent to the AA calling or folding.
It's possible the clairvoyant is not ahead
often enough on the flop and turn and this
game is not worth playing.

[jogsxyz]

[ QUOTE ]
A. Fold all hands.
B. Call with any two cards, and re-raise with KK, QQ, and JJ.
C. Call with any pair or suited connector.
D. Call with any two cards, do not re-raise with anything.
E. Call with any two cards, and re-raise only with KK.
F. Call with any two cards, and re-raise only with AA.

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Here's the choices for answers from the test.
It must be right to call or raise with the other two aces.
Therefore folding all hands is clearly wrong.
B. and E. seem wrong. F. is wrong because if you
only reraise with the other two aces SB knows what
you have.

That leaves C. or D. There's far too many starting
hands which have less 10% equity against aces.
Calling any two just doesn't seem right.

The tester is telling us that C. is the right answer.

[Nichlemn]

Here's some thoughts:

In a situation where you could get to the river immediately, you would be even money money for the hand if you could make a post sized bet and were 33% to get ahead of the Aces. You would make a PSB every time you improved, a PSB half that time (1/6) to make your opponent indifferent to call, and surrender-checked the remaining 50% of your hands.

If you could make much bigger than pot sized bets, your hand would only need to be good slightly more than 25% of the time for you to be even money against the Aces. Slightly less than half the time you surrender-check your hand, the rest you make an enormous bet, betting for value slightly more than half as much as you bluff to make the opponent indifferent to call.

Now this is not only factor. The three streets of betting and potential for semibluffing makes this different. I think a similar principle applies though: bet based on the equity of your hand to make Aces indifferent to call. Now the flop/turn parts seem to complicate this greatly.

It's a given that the opponent to Aces is always going to bet their hands with greater than 50% equity against them on the flop and the turn. It seems that hands with over 33% equity against Aces should always bet as well even if an opponent always calls: given the nature of the river bet as outlined above, any amount of money put in as a 33%+ favourite earlier is +EV. Though I haven't worked it all out, hands with less than 33% equity should still bet a certain % of the time to make Aces indifferent to calling (but what level is that exactly, with the implied odds making not simply 33% equity against the opponent's range?)

Further complicating things is the texture of the board will give random hands different equities against Aces, changing %s making Aces indifferent to call, and the fact that two new cards change the equity twice. Working out exactly what the result of this is will be needed to figure what %s of the time the opponent needs to bet.

This seems solvable, but it'll take some effort.

[Nichlemn]

A similar question: KK versus any two cards. If you always raised against them with AA and never anything else, they can instantly read your hand like it is in here. But if you occasionally raised with other hands and limped with Aces this could be averted. This adds some preflop strategy to the problem.

[Yepitis]

Maybe I am a retard but...

a) AA

b) fold

c) raise

Really, no matter how good you may be you can't beat AA with random cards in the long run. If the Aces always raised they will win over a life time.

I'll take anybody up on this... up to the cost of my house and 401K.

[Nichlemn]

Simplified simulation:

Both players ante 1 dollar (simulating preflop). One player is dealt a card saying "Win" 1/12 of the time and "Lose" 11/12 of the time. This player can make up to three pot sized bets (simulating each street) or surrender (simulating checking/folding, though this is somewhat different) and the opponent calls or folds. Who is the favourite? They are even money.

The player with the card should bet the entirety of the time they have "Win" and 11/24 of the time they have "Lose" as a bluff. The rest of the time (1/2) they surrender.

Bet/ Surrender
Winner/ Loser/ Loser
1/12/ 3/4/ 1/2

The opponent is indifferent to call or fold and as such should do so randomly.

The next "street", obviously only consisting of hands the opponent has called the first street with, is now weighted at 1/6 "Win" and 5/6 "Lose".

Bet/ Surrender
Winner/ Loser/ Loser
1/6/ 1/3/ 1/2


And so the same for the next round:

Bet/ Surrender
Winner/ Loser/ Loser
1/3/ 1/6/ 1/2


Summary

When making a PSB with a winner or loser, it is even money if said player holds "Winner" 1/3 of the time. Therefore, since an opponent is indifferent to calling a bet that will lead to having to another indifferent betting round, they will be indifferent to calling all the way up to the first betting round. So if an opponent has a 1/6 chance of holding a winner and bets, and you call with one betting round left, they will hold a winner on this final round 1/3 of the time and thus be even money, so you were indifferent to calling in the first place. Therefore it would be 1/12 with three betting rounds to go, and so on.

This seems to indicate that very roughly, you need over 1/12 equity to make calling against Aces +EV.