How to calculate risk premium?

    • chrupens
      chrupens
      Bronze
      Joined: 01.03.2011 Posts: 168
      Hi,

      Today I watched pzhon's video about calling allins and unfortunately I didn't clearly understand how to calculate risk premium.

      First of all I have to calculate $reward:$risk ratio. Assuming situation:

      CO: 3000
      BTN: 1000
      SB: 6000
      BB: 3000

      With blinds 150/300

      If I call and win I increase my $Eq from 26,5 to 36 so the reward is 9,5$
      If I call and loose I go from 26,5 to 0 so I am risking 26,5$

      The ratio reward/risk is 0,35. I get to this point and don't know what to do next.

      According to ICM explorer I get risk premium ~25%.

      Thanks for any help.
  • 4 replies
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      It looks like you are assuming that the chip leader is pushing onto the big blind. You will get different results with other combinations.

      The idea of the risk premium is useful because you can estimate it before you know the equities of folding, winning, and losing. If you estimate the risk premium, then calculate the chip odds, you add the two to get the equity you need.

      To calculate the risk premium instead of estimating it, you calculate the equity you need for calling to break even in $, and subtract the equity you need for calling to break even in chips. You need 70% ~ 25/36 equity against the chip leader for calling to break even in $. Your numbers are a little off because you only risk the 25% from folding, not 26.5% from taking the blind back. You do not have the option to take the blind back. The reward is 11%, the difference between doubling up (36%) and folding (25%).

      Again, in practice, what you want to do is remember that the second stack has a high risk premium against the chip leader on the bubble. With equal stacks on the bubble, the risk premium is about 15%. The second stack may have a risk premium of 20-35% against the chip leader on the bubble. You estimate the risk premium, hopefully getting something close to 25%, and add this to the 45% chip odds for a 10 bb small blind push to get about 70% equity needed. That makes it an unexploitable fold with AKs, a fold even if you put the chip leader on a random hand.
    • kiromanAAKK
      kiromanAAKK
      Bronze
      Joined: 08.10.2009 Posts: 4,022
      Well, pzhon u must have a huge head to keep all this stuff inside! :D
      Thanks for your great explaination, btw :)
    • chrupens
      chrupens
      Bronze
      Joined: 01.03.2011 Posts: 168
      Originally posted by pzhon

      The idea of the risk premium is useful because you can estimate it before you know the equities of folding, winning, and losing. If you estimate the risk premium, then calculate the chip odds, you add the two to get the equity you need.

      To calculate the risk premium instead of estimating it, you calculate the equity you need for calling to break even in $, and subtract the equity you need for calling to break even in chips. You need 70% ~ 25/36 equity against the chip leader for calling to break even in $. Your numbers are a little off because you only risk the 25% from folding, not 26.5% from taking the blind back. You do not have the option to take the blind back. The reward is 11%, the difference between doubling up (36%) and folding (25%).
      Thanks for your response pzhon. You say it's useful because I don't need to know eq of folding winning and losing, but in order to calculate sie equity to break even in $ I need to know the eq $ of folding and eq $ of winning (in the example its 25/36 ~ 70%) so it's not easy to estimate it at sight. Still, probably something I don't understand :( Could you provide the calculations step by step?
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      You aren't expected to do the exact calculations at the table. To build your ability to estimate the risk premium, you perform the exact calculations on many examples, and then notice patterns. For example, you might notice that the risk premium is low when you cover the pusher by a lot, even when it is the bubble, or that the risk premium increases on the bubble when a player with a short stack has already folded. You might notice the risk premium is never negative, even if you have the chance to knock someone out.

      My program ICM Explorer does the exact calculations, and computes the risk premium for you. This is the output for calling a small blind push with the stacks you give:

      Fold: 2700 chips, 0.2524, SD: $14.56
      Win: 6000 chips, 0.3604
      Lose: 0 chips, 0
      Tie: 3000 chips, 0.265

      Equity needed: 70.04%
      Chip odds: 45%
      Risk premium: 25.04%
      Chips gained by marginal call: 1502.34.
      Ties count as 73.52% of a win.
      SD of marginal call: $18.42.

      If you want to check the calculation, you could take the values for folding, winning, and losing, and compute that the equity needed to call is (fold-lose)/(win-lose) = (.2524-0)/(.3604-0) = 0.7004. Then you subtract the chip odds, also calculated by (fold-lose)/(win-lose), with all outcomes evaluated in chips: (2700-0)/(6000-0) = 0.45. 0.7004-0.45 = 0.2504. I don't think you need to be able to build your own calculator to use one, though. It is better to focus your attention on what your opponent's range might be. The risk premium simplifies the estimate of the equity you need because you don't have to evaluate the equities from folding, winning, and losing.