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Settlements

Posted By: Henrik Bukkjaer
Date: Tuesday, 5 June 2012, at 3:51 p.m.

In Response To: Settlements (Barry Silliman)

Ohh, mistake number one: Asking a mathematician about how to act in a real world setting... :-)

He might even try to calculate the proper settlement here, based on the cube value and the 10 numbers that doesn't bear off!

All without asking the involved players what they would do with the money should they win, and how much it would hurt them to loose.

Instead, ask an economist, and he'll tell you about the "utility of money" - and probably mention the Sct. Petersburg Paradox (which was solved by a mathematician by the way).

So, to answer your question Seth:

Start calculating the expected value here, the average number of points you would win.

Then calculate the best and worst outcomes and their probabilities.

Think how much you would like/dislike these alternatives - how important those last dollars are to you, or how much you can afford to loose, and then adjust the initial expected value according to your personal "utility curve".

If the stakes are small enough, there's nothing to adjust, unless it means a lot to you (pride-wise) to come out of the session as a winner, in which case your current score affects the decision!

---------------

Example:

Say this is the fifth game in the session, and you're playing for $1000 per point - your up +12 on the score sheet after the first 4 games.

The reason you sat down playing for so high stakes, was that you needed $26000 to pay for some operation you need at a hospital. You only had $8000 in cash, and decided to take a chance ($8K or nothing wouldn't really do much difference on your health).

So now your opponent offers to settle this for +6 points to you (knowing that he stands to loose a little more than 7 points, should you decide to roll).

Should you accept the settlement "costing" you more than a grand compared to expected value?

Off course you should! You will end up with exactly the $26K you need that is so important for you.

Now, say you had +2 going into this game, and he offers you 8 points here (you get a free $800+ accepting this) - you should seriously considering to turn down the offer and simply play your chances...

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