2010-07-09 Redouble/Answer

For money, if white redoubled this, it would be a solid Beaver, because White is not favored here.  In fact, as you can see from the evaluation below, White only wins this game about 39 percent of the time.  But that's enough to double at this score!

It's all about risk/reward.  It's about what kind of match winning chances White has if he doesn't redouble and loses, compared to what happens if he doesn't redouble and wins, and you compare that to what happens if he does redouble and loses and does redouble and wins. 

In simple terms, if he redoubles and wins he has 100 percent equity...he's won the match, and if he redoubles and loses he has 0 equity, as his opponent has won the match.  So is he better off betting the match on the next roll, where he has 39%?  Well, if he doesn't double and he loses he has about 18 percent equity in the match, and if he doesn't double and wins, he has about 59% equity.

So there is a formula that we can use, over the board, to give us the answer.  It is risk divided by risk + reward.

Don't redouble and lose the game makes the score 1-4 Crawford with about 18% MWC.  Do redouble and lose the game loses the match with 0% MWC.  So the risk or loss from redoubling is 18%.


Don't redouble and win the game gives you a 3-2 lead with about 59% MWC.  Do redouble and win wins the match  with 100% MWC.  The gain or reward from redoubling is therefore 41%.


The minimum redoubling point is risk/risk + gain = 18/18 + 41 = a little over 30%.  You've got 14/36 winners which is around 39%.  Since you're over your minimal redoubling point and this is the last roll of the game, redoubling is correct.


If it seems wrong to redouble as an underdog, here's proof that it's correct.  If you don't redouble, 14/36 you'll win this game and have around 59% MWC.  Over the board, I'd round 14/36 to 40% and 59% to 60% since 40% x 60% is a lot easier to multiply than 39% x 59%.  40% x 60% = 24% MWC.  If you don't redouble and lose this game (22/36), you'll be down 1-4 Crawford with about 18% MWC.  OTB, I'd round 22/36 to 60% and then multiply 60% x 18% = 10.8% MWC.  So your MWC if you don't redouble now is 24% + 10.8% = 34.8%.


If you do redouble, your MWC are simply 14/36, about 39%.  So redoubling as an underdog is correct in this position because it increases your MWC from 34.8% to 39%, a 4.2% increase.