Ace and a Deuce heads-up

[Fnord]

You're in a heads-up SnG with the button and are delt an Ace and a Deuce offsuit.

How large must the blinds be relative to the short stack for it to be profitable to push all-in?

If the blinds are smaller than that amount, is your hand worth playing? Under what circumstances? If the other player has comperable post-flop skills?

How does being suited change the situation?

[Manomanman]

What is the probability that his hand is any pocket pair?

[Fnord]

What is the probability that his hand is any pocket pair?

... or a bigger ace. You're on the right track...

[Fnord]

Let's say the blinds are such that folding is better than calling with a worse hand. Also, our opponent is Super Man and because of his x-ray vision he will only call with a hand that dominates ours. Then we can work backwards from the perfect play number to guess what the number might be if a worse hand calls.

Here is my math for when it's break even against perfect play:

hands dominated by
AA - 3 ways
22 - 3 ways
KK - 33 - 6 ways each (11) for 66 ways
AK - A3 - 12 ways each (11) for 132 ways

132 + 66 + 6 = 204

total hands left
50 * 49 / 2 = 1225

0.167 better hand
0.833 worse hand

We beat a better hand 25% (conservitive)


Let X be the big blind
Let Y be the short stack

EV is
(best hand * amount won on fold) + (worst hand * (amount won - cost))
(0.833 * 1.5x) + (0.167 * ((0.25 * 2 * y) - (y - 0.5X) ))
(0.833 * 1.5x) + (0.167 * ((0.5y - (y - 0.5X)))
(0.833 * 1.5x) + (0.167 * (-0.5y + 0.5X))

Solve for an EV of 0
(0.833 * 1.5x) + (0.167 * (-0.5y + 0.5X)) = 0
(0.833 * 1.5x) + (0.167 * (-0.5y + 0.5X)) = 0
1.2495x - 0.0835y + 0.0835x = 0
1.333x = 0.0835y
y = 15.96x

[Toasty]

If I'm following this right:

hands dominated by
AA - 3 ways
22 - 3 ways
KK - 22 - 6 ways each (12) for 72 ways
AK - A3 - 12 ways each (11) for 132 ways

KK - 22 - 6 ways each (12) for 72 ways Shouldn't this be KK-33?

Also, I'm sure I've read a few of these posts over at 2+2 and the more important question in these scenarios are what hands will an opponent call with.

[Fnord]

KK - 22 - 6 ways each (12) for 72 ways Shouldn't this be KK-33?

Fixed.

Also, I'm sure I've read a few of these posts over at 2+2 and the more important question in these scenarios are what hands will an opponent call with.

I think we can work backwards from the perfect play number given the value of just taking the blinds outright. Obviously the more often they fold 33, A3 or call with Kx the smaller the blinds need to be for this play to be correct.

[Toasty]

I'm pretty amazed how well A2os does against a random hand, how many coin flips are left with the rest ?

am I right in thinking anything from 43os will be close to a race ?

[Fnord]

I'm pretty amazed how well A2os does against a random hand, how many coin flips are left with the rest ?

am I right in thinking anything from 43os will be close to a race ?

Against JTs it's nearly a coin flip, but against most hands it's around a 60% favorite.

A lot of its value is from the unpaired Ace beating a hand that horribly missed the board. Hence the question of if it has any positive value if you play it in a no-limit game outside of pushing pre-flop.