[keylime]

Bridge is a great game to do outcome predictions and conditional probability on because of the changing odds as conditions warrant. Ben's analysis was so lucid that non-math folks could understand it. I'll spare you all the combinatorics that are involved - isn't this just the best game in the world?

[mpefritz]

inquiry, on Mar 12 2004, 06:00 AM, said:

mpefritz, on Mar 11 2004, 10:12 PM, said:

I think Ben's original problem is a good one in getting newer players to think about how odds change as more information is available.

Thanks, that was the point exactly....

BTW, how close are you to fully agreeing with my solution now?

Ben,

I am not fully agreeing with your analysis of AK32 654. This is the beginner/intermediate bridge discussion.

Let me ask you this Ben.

You are playing against two Beginners and (for some reason) you cash the AK of this suit and LHO plays 8Q and RHO plays 79. What are the chances of a 3-3 split at this point. I propose to you it is as close to zero percent as possible, BECAUSE most beginners will play their lowest card available when following suit.

So the roundabout point I have been prodding Ben to mention is that when players ALWAYS give count or ALWAYS play their lowest of equals, AND the declarer knows (or highly suspects) this, you are giving the declarer information that will let him better calculate odds.

All of Ben's analysis assumes two things:
1) Each defender will randomly play from equals.
2) Each defender in these problems KNOWS that their cards are equals.

Number 1 is iffy in most beginner play, and number 2 is very difficult even for the best defenders. If they are good enough to realize that all of their cards (QT7, say) are equals, then they have probably assigned some meaning to the order in which they are played.

Now in the AK32 654 example, if the declarer closed her eyes and after 2 rounds asked if both had followed AND not known what the cards were, then Ben's analysis of the 3-3 4-2 chances (42+ to 57+) would be correct. But that is not how the game is usually played.

fritz

[1eyedjack]

luke warm, on Mar 10 2004, 08:03 PM, said:

this reminds me of a riddle i once read... i only give it as preamble to my comments...

you're at a table with another person... he places a coin under one of three upside down cups... he asks you to choose which cup you think the coin is under (we'll assume you didn't *see* him place it heheh)

after you choose, he lifts one of the three cups and shows it to be empty underneath... there are now 2 cups, the one you chose and the other... he now gives you the choice between changing your pick to the last remaining cup or staying with your first pick... do you change?

the original odds were 2:1 against you choosing the correct cup... those odds did not change after you chose, simply because he showed you one of the two that was not correct... so the winning choice is to change cups... the odds were against you when you chose, therefore by changing you placed them with you

on the problem above, i think the original odds of clubs dividing 4/2 are greater than them dividing 3/3.. if so, the odds for any one card (the queen in this case) being with the 4 are 2:1... i don't see how these odds changed, all things being equal...

I think the answer (whether to change) may depend on whether the operator is required to offer you the choice to change or whether he may offer you that choice at his discretion. I could be wrong.