| Posted by: Cheetah at December 6, 2007, 10:09 pm | | Topic: Red Zone strategy discussion Forum: Card Chat |
Quote: Originally Posted by Bentheman87
Also here's another question to think about. How small does your M have to be before it's correct for the big blind to call your all in with any two cards, assuming he knows that you don't have a big pair like AA KK QQ or JJ since it's so unlikely given your desperate situation.
The chance to get a big pair dosn't depend on how desperate you are. So they should be included as well. So I think you are asking: When should the big blind call if they know you are pushing with any 2 cards?
If we ignore the fact that the big blind is already posted, then the pot odds would be 1:1 regardless of the size of the small stack. In that case, a big-stacked big blind can call whenever the equity in the pot is greater than 50%. The following hands satisfy this condition(the numbers are for the lowest hand in the group):T8+: 50.375%J7+: 50.343%Q5+: 50.782%K2+: 51.184%A2+: 55.541%Of course these numbers change a little for suited s unsuited, but the effect is only 1-2% in either direction.
For smaller stack sizes of the small blind, the pot odds deviate quite a bit when we take into account the posted big blind. For example, if the small blind has 3BB after posting the SB, then the pot odds for the big blind are:
pot odds = amount to win/amount to call = (1BB + 0.5BB + 3BB)/2.5BB = 1.8
As can be seen, this is significantly bigger than 1 if we ignored the posted big blind. Pot odds of 1.8 correspond to the following required pot equity:
Required pot equity = 100%/(1+pot_odds) = 100%/(1+1.8) = 35.714%
The above equity is satisfied by the following hands:43+: 36.020%53+: 37.122%63+: 36.942%73+: 37.461%83+: 38.331%92+: 39.927%We can see that there is a dramatic change between calling profitably a small stack and a big stack just because of the posted big blind. The general formula for the required odds to call is:
Pot odds = (Stack + 1BB)/(Stack - 1BB)
where Stack is the stack of the small blind before posting the small blind.
If there is more interest in this topic, please let me know and I will calculate what hands in the big blind can call profitably a small blind desperation push as a function of small blind stack.
Please note that the above is alid only if the big blind has a big stack so that decisions are made solely on cEV. If the big blind had, say, twice the stack of the small blind, it would be incorrect to call so liberally because the $EV comes into play. If the big blind loses, it will become desperate and its $EV would be much worse with a tiny stack.
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