Risk Premium on Push Ranges
I'm trying to work out how to mathematically adjust a push range because of risk premium.
With calling, I see it's just adding the risk premium equity to my pot odds calling equity.
In cash games, I think of semi-bluff adjustments with this:
If I'm semi-bluffing, I subtract that equity from the final pot from my bet. Then compare that amount to my reward and see if I think villain is folding that often.
Example:
I push $100 into a $100 pot and believe I have 25% equity when called. So, I own $50 when called.
So I subtract that $50 from my $100 push, and get I'm risking $50 to win $100 with my push. At 2:1, I need villain to fold at least 33% of his range.
I'm hoping there's a way to have a shortcut like that to use to adjust my pushing ranges based on risk premiums. I've tried simply subtracting my risk premium from my equity vs his calling range, but that's not matching what i'm finding in software tools. Any ideas?
4 Replies
If I correctly interpret your situation, you’re considering both card and fold equity along with your push size for deciding how to act. Assuming villain either calls or folds, the EV equation is EV= F*P+(1-F)*(E*(P+2B)-B), where
P= Pot before you bet; B= your bet size; F= fold equity; E= card equity
By setting EV to 0 and assuming known P, you can find any one of the 3 variables given the other two are known.
Example: For your problem P=100, B=100, E=25%
Then EV = F*100 +(1-F)*(0.25*(100+2*100) – 100) = 0
Solving for F you can show that F= X/(1+X), X= B/P-E*(2B/P+1)
Here X= 100/100-0.25*(200/100 +1 ) = 1-0.75 = 0.25
Then F = 0.25/1+0.25) =0.20
Check: EV=0.20*100 + 0.80 *(0.25*300 - 100) = 20+0.80*(-25) = 0
Of course, you can derive the critical equations for the other variables (and they are simpler) and also set EV target values other than 0.
I hope this provides insight into the issue you are facing.
Thanks for the reply. So..apparently I've been wrong about something here, and I can't put my finger on where. To calculate the fold equity % needed for an EV of 0, I've always used:
x = Fold% * Pot + (1-Fold%) * (Win%*WinAmt - Lose%*LoseAmt)
So, in this case:
x(100) + (1-x)(.25(100) + .75(-100))>0 = 0
And I end up with x = .33
I've thought this means he must fold 33% of the time for me to have an EV of 0. However, I see your answer of .2 is the correct one.
Where am I going wrong?
Ah...I see this is x(100) + (1-x)(.25(200) + .75(-100))>0
x = .2
So, we're the same there.
But, what I'm after from here is to take into consideration the bubble factor in a push/fold decision.
To continue with our same example, let's say I have a bubble factor of 1.5 versus the opponent. So, I have a 10% risk premium.
How do I adjust this equation to see how often he needs to fold? Do I just reduce my 25% equity to 15%?
I’m not in a position to directly address your question so I’m posting a section of an article I wrote on the bubble factor.
We know that in cash games, for an all-in bet, the math decision for a profitable move is to call the bet if your equity is at least Bet/(Bet + Pot) = 1/(PO+1), where PO are the pot odds.
For a tournament the equivalent strategy is to call if your equity is greater than 1/(PO/B+1), where B is the bubble factor. Since B is always greater than 1.0 (losing chips costs more that gaining chips – an ICM precept), we see that you need more equity in a tournament to call the bet than for a comparable situation in a cash game – reminder- this is based solely on the math.
