[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Philosophical Question on 'Wrong D/P is not an Error'

Posted By: NJ
Date: Wednesday, 9 December 2009, at 3:03 a.m.

In Response To: Philosophical Question on 'Wrong D/P is not an Error' (Christian Plenz)

Let's examine 3 possible cases.

  1. Player B will take 100% of the time and Player A knows it.
  2. Player B will pass 100% of the time and Player A knows it.
  3. Player B will flip a coin to decide, and Player A knows it.

In case 1, it's clear that No Double is correct, and Double would be a -5% error (80% vs 85%).

In case 2, the expected value of doubling is now 87%. Therefore the correct action is Double. If you did not double you would be making a -2% error (85% vs 87%).

In case 3, the expected value of doubling is 83.5%. Therefore the correct action is No Double (85% vs 83.5%). If A doubled, it would be a -1.5% error, regardless of how the coin flip turned out.

I think these examples show that player B's strategy does affect the expected equity of doubling. However, the problem is whether player A can accurately predict player B's likelihood of take/pass. In the given example, player B would need to pass at a rate of 5/7 in order for player A to be correct in doubling. Case 3 shows that even if player A doubles and player B mistakenly passes, it doesn't necessarily mean that player A made the correct choice if player B's likelihood to pass was less than 5/7.

The other question is: what is B's error when A doubles? I would consider it to be:

  1. 0%
  2. -7%
  3. -3.5%

Personally, I feel that we should always measure errors compared to perfect play. Once you start taking into account "expected errors" from your opponent, the equities and errors become very subjective. So in this example, on a double/pass I would say that A made a -5% error and B made a -7% error.

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.