Question: When should I accept an opponent's offer to double the value of the game?
As a general approach, imagine you will be playing many games from this exact position though they will each end differently because of the random rolls of the dice. Put differently, you should use a disciplined approach to such decisions rather than your expectations for the specific game.
To illustrate: You believe you have only a 30% chance of winning this game and your opponent has offered to double the value of the game. Well, we've already said you expect to lose this game. But using the general principle, you should accept the double anyway!!
Why? If you played 100 games from this position, you would expect to lose 70 of them and win only 30. If you declined the double in all 100 games, your score from those games would be -100. However, if you accept the double in all those games, you're expecting to have 70 cases when you lose double (call that -140), and 30 cases when you win double (call that +60). Adding the winnings and losings gives -80 (-140+60). So, over 100 games, you believe you would score -80 from always accepting the double, and -100 from always declining.
Neither outcome is desirable!!! But you reduce your losses, and increase your success, by accepting doubles when your chances are only 30%.
The terminology "Cube Strategy 101" and "Lesson 1" imply that there's a whole lot to be said. So long as there is interest and participation from others, I will make additions.
Note that my first message in this thread didn't really answer the difficult question of when one should accept a double. It merely provided the logic of accepting a double - though expecting to lose - when one believed the chances were 30% for winning.
The first, tiny step in answering your question is to take that calculation from that first message and turning it around: At what probability of winning would the expected losses from accepting the double equal the expected losses from declining the double? The answer is 25%. Then our 100 cases of declining yield 100 losses (-100) and our 100 cases of accepting yield 75 doubled losses (call that -150) and 25 doubled wins (call that +50) or a net result of -100.
There's a whole lot more to say, but this is one idea you may find helpful.
Re: Cube strategy 101 -- Lesson 1
Message #400 Replies: 0
posted by heartsvertigo (Bob Bowman) on 04/18 at 05:19
i just want to point out that what you posted, although correct in money play, will not always be right in match play. in match play, your winning chances in the particular game must be compared to the current score of the match. in another thread, frolind posted a great link that delves into match equity(among other things), i am taking the liberty of copy/pasting it below http://www.bkgm.com/articles/mpd.html for just the match equity, go to http://www.bkgm.com/articles/mpd.html#using_table
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