An AA offer

[Chris Daddy Cool]

in your dreams you're paid a visit from the poker fairy who makes you an offer with two choices.

choice 1
for the remainder of your life you'll recieve AA twice as often as expected, but you will recieve all other pairs half as expected.

choice 2
for the remainder of your life your winrate with AA will be twice as much as expected, but your winrate for all other paris will be half of what is expected.

Which one is a better offer?

And are these choices +EV or -EV?

If -EV, what is the minimum correct ratio to make it +EV, if at all possible?

[NMcNasty]

I think both choices are - EV, but if I had to choose between the two it would be choice two. I think it might be a trick question though since your overall winnings with pairs is times received x winrate. So, (1/2)Times Received x winrate = Times received x (1/2)winrate. However, if you play more hands you gain information on your opponents which can be used to your advantage later on.

[Monty Cantsin]

Seems like we should start by figuring out if there's a difference between:

1) doubling the frequency of AA
2) doubling the winrate for AA

and, if so, which one is better.

In both cases you can expect to win twice as much money from AA. The only difference is that in (1) this extra profit comes from additional AA hands that are displacing the hands you would otherwise get, each of which has a small but positive expectation. So, by themselves, it seems we should prefer (2).

Then we look at the costs:

1) halving the frequency of 22-KK
2) halving the winrate of 22-KK

Again, we expect to earn half as much money from our pairs in both cases. But in (1) the missing pairs are filled in with random hands, each of which is slightly +EV, so the cost is offset slightly.

Putting these together we see Choice 1 has a slightly better payoff and slightly higher cost, and Choice 2 has a slightly worse payoff and slightly lower cost. So I'm going to say: it's close!

I do not want to take these deals. Because I think the rest of the pairs together add up to more profit than AA so in each case the cost is higher than the payoff.

What'd I miss?

/mc

[UATrewqaz]

Where does this poker fairy live and why does she hate me?

id rathar double my small pairs or small pairs win rate than AA.

This is very -EV, going by my poker tracker:

frequency of AA: 75
BB per AA: 2.94
total BB won: 220.5

frequency of KK-22: 879
BB per pair: 2.49
total BB won: 2188.71

so, to double either the frequency or win rate of AA in exchange for halving the freqency of other pocket pairs would end up costing me about 800BB every 10k hands, or -8BB/100. so actually, if you double your freqency of Aces while cutting the amount of times you get other cards, it would make poker an unbeatable game.

[Monty Cantsin]

CDC, were you getting at something with this question?

Just curious.

/mc

[pudley4]

[ QUOTE ]
frequency of KK-22: 879
BB per pair: 2.49


[/ QUOTE ]

There is absolutely positively no way in the world that this stat is anywhere close to correct.

[Monty Cantsin]

Yeah, that's clearly a mistake.

/mc

[ QUOTE ]
[ QUOTE ]
frequency of KK-22: 879
BB per pair: 2.49


[/ QUOTE ]

There is absolutely positively no way in the world that this stat is anywhere close to correct.

[/ QUOTE ]

What is typical for aces and smaller pairs then?