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Say you are facing an all in with AKs and put your opponent on AA, KK, or QQ

What odds do you need to call?

2

propoker tools says:

Hold'em Simulation 82,190,592 trials (Exhaustive)
Hand    Equity  Wins    Ties
AxKx    34.59%  28,123,620  605,616
QQ+     65.41%  53,461,356  605,616

looks like about 2:1

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  • call if the pot is offering you 2:1 or better – Ray Tayek Apr 4 '17 at 3:07
  • sorry, i mised it – Ray Tayek Apr 4 '17 at 3:47
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On related question I ran the numbers and thought it might be of value

Since you have blocker on AA KK you will see them less
1/4 AA
1/4 KK
1/2 QQ

Odds against those hands
AA 1/8.5
KK 1/3
QQ 1/2

In net (1/4/8.5 + 1/4/3 + 1/2/2) = 0.36

1 is pot and b is the bet you need to call
EV 0 = -b + (1/4*1/8.5 + 1/4*1/3 + 1/2*1/2)*(1+2b)
b/(1+2b) = (1/4*1/8.5 + 1/4*1/3 + 1/2*1/2)
(1+2b) / b = 1 / (1/4*1/8.5 + 1/4*1/3 + 1/2*1/2)
1 / b = 1 / (1/4*1/8.5 + 1/4*1/3 + 1/2*1/2) - 2

b = 1.32 of the pot
Or you need to be getting about 1.757:1

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  • I think it's simpler to use the formula 2b + p = ob where b is bet (your stack) p is pot and o is odds of losing. o = (8.5 * 1/4) + (3 * 1/4) + (2 * 1/2) = 3.875. Plugging that into the equation we get p = 1.875 or 15/8 which is close to what you got. Am I missing something in this calculation? – JimmyJames Nov 11 '16 at 15:52
  • When you say p = 1 simplifies, are you saying take the reciprocal? You can calculate how small your bet needs to be in terms of the pot or how large the pot needs to be in terms of the bet. I prefer the latter since it is easier (for me) to do multiplication in my head than division. – JimmyJames Nov 11 '16 at 16:06
  • I'm relaxed (about this anyway.) I thought you pointed that out because you felt it was important. – JimmyJames Nov 14 '16 at 14:55
  • Sorry I don't follow your math. Can you explain what is wrong with the approach I gave? We are trying to calculate when the odds are even, right? – JimmyJames Nov 14 '16 at 18:09
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    This conversation has been moved to chat. – Toby Booth Nov 15 '16 at 23:53
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Well taking away the math, if you have a tell on that player you should fold as you are an underdog against all three hands.

Mathematically speaking, if you are heads up then in tournament for instance it makes sense to take a coin flip vs QQ (56%-44). For an all-in, AK is a big underdog to KK (30%-70%) and it is even worse vs AA (15%-85%).

If you are a novice I would advice you to never fold AK in tournaments in all-in situations. In most situations you will face coin flips but sometimes you will be a big favourite vs AQ-A2. Only AA and KK are scary cards but you have blockers vs both.

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    Can be an underdog and it still makes sense to call if you are getting proper odds – paparazzo Nov 10 '16 at 0:51
  • if you are facing allin preflop vs one player I doubt you will ever get right odds to call vs KK AA unless your Harrington's M is in a desperate situation (tournaments) – Kanan Farzali Nov 10 '16 at 0:54
  • This can happen if there are other players who bet/call and then fold to e.g. an all-in by the big-blind. – JimmyJames Nov 11 '16 at 16:12
  • @JimmyJames Yes, whether the other players have folded or not. Or if it's a tournament and you have the other player covered and a chance to knock out a short stack. So many consideratons. – user1934 Nov 12 '16 at 16:35
  • @Michael I guess it's not called out explicitly but it's strongly implied that there is only one opponent left. It would be a different odds calculation otherwise. – JimmyJames Nov 14 '16 at 14:53

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