This article originally appeared in the July 2001 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
The following very interesting and instructive position came up in my
second round Masters match in Las Vegas last month:
Ed had a nice lead in the match, and he was doing pretty well this game also as another of my speculative early cubes was in the process of going sour. Should Ed send it back to 4?
Ed has a fine position. If he rolls a four and covers the blot on the three point he will have a solid six-prime, and it will be difficult for me to win the game. If he rolls a five he can at least cover the blot and still have a commanding advantage. Even if he rolls badly, his five-prime will still be staring me in the face.
For money or at an even match score, this would be a fine redouble. Ed has plenty of threats, and if he carries out the big threat of making the six-prime he would lose his market by a mile. In addition, is it so clear that I would even have a take? Probably I would, but it isn't immediately obvious. It wouldn't be a shock if I had a pass, or if I passed even when it was a take. Definitely a fine money redouble -- it would be the take, not the double, which would be in question.
Does the match score make a difference? We all know that we should tend to be more conservative with the cube when ahead in the match, but how far ahead do we have to be? Ed still needs 8 points to win the match. This means he can definitely use all 4 points from a redouble, and can even use all 8 points from a gammon. It might seem that Ed does have a proper redouble, in spite of his lead in the match.
The above arguments may look sound, but they leave out one slight detail: The cube may not stay at 4 very long. Let's look at things from my point of view assuming I have taken the 4-cube and am considering sending it back to 8. For starters, let's assume that there won't be any gammons (which is certainly not true). We don't have a 16 away, 4 away on my chart, but extrapolating from the 15 away, 4 away number it looks like about 6%. Therefore, we would have:
I don't double and lose: Behind 13-1 (16 away, 4 away), 6% equity.
Thus, on the gammonless assumption, I would be risking 6% in order to gain 19% on my redouble to 8. We can see immediately that I wouldn't need much of an excuse to redouble.
Let's throw some gammons into the picture and see what happens. As a guess, let's suppose that 25% of each side's wins are gammons. This means:
If I don't double and lose, I will be behind 13-1 75% of my losses and I will lose the match 25% of my losses. Thus, my average equity will be 4 1/2%.
If I double and lose, I lose the match -- period.
If I don't double and win, I will be behind 9-5 (31% equity) on 75% of my wins, and I will be tied at 9-9 (50% equity) on 25% of my wins. That comes to about 36% equity on average.
If I double and win, I will be tied at 9-9 (50% equity) on 75% of my wins, and will win the match (100% equity) on 25% of my wins. That comes to an average equity of about 62 1/2%.
Thus, I will be risking 4 1/2% equity to gain 26 1/2%! You won't find odds that good anyplace else in Vegas. It is obvious that I would not be making a big mistake by redoubling immediately regardless of what Ed rolls. The only reason to not redouble is if it were impossible for me to lose my market whatever happened on the next exchange (which would be the case if Ed did complete his six-prime). However, it is clear that if there is any chance that I could lose my market on the next exchange, I must redouble.
This sheds an entirely different light on the position. If Ed redoubles to 4, that means that every time he loses the game he will be losing with the cube on 8! I am not going to give him a chance to escape cheaply. If there is so much as 1 exchange in 1296 which would cause me to lose my market, that cube is coming flying over. Thus, by redoubling to 4 Ed isn't really turning the cube to 4. For all practical intents and purposes, he is turning it to 8.
Can this possibly we worth the risk? Our intuition screams no, and our intuition is quite correct. If this is a take (or even close to a take) for money, it has to be a huge non-redouble at this match score. To convince ourselves of this, let's grind out the numbers. For simplicity, let's assume that I will always redouble to 8 immediately. Keeping our 25% gammon assumption for both sides, here is how things look from Ed's point of view:
Ed doesn't double and wins: He is either ahead 11-1 (6 away, 16 away) for
about 88% equity, or he is ahead 13-1 (4 away, 16 away), for about 94%
equity -- averaging out to 89 1/2% equity on our 25% gammon assumption.
Thus, on balance Ed would be risking 37 1/2% in order to gain 10 1/2%. He would be giving almost 4 to 1 odds with his recube. Even if this were the last time he would ever be permitted to double this game, his position isn't that good -- no way he is winning this game over 75% of the time. And it isn't close to his last chance to double. If he makes his solid prime and I do nothing special, then maybe he has a double -- that is an entirely different problem. Here, it isn't close.
Well, Ed actually did redouble. I was stunned! After starting at the position for a bit to make sure there wasn't something about the position I was missing, I happily snatched the cube up, polishing it in preparation to send it back if I so much as saw daylight.
Ed rolled 2-1. Not his best. He did the best he could, playing 7/6, 3/1*. This way I couldn't hit and get to the edge of the prime at the same time. The position with me on roll holding a 4-cube was:
Do I see daylight? You bet I do! How about double-aces for me, and a flunk by him? That would certainly qualify as a market loss. There might be others, but I didn't need any more. As we have seen, any market-losing sequence is sufficient for me to justify redoubling. I instantly turned the cube back to 8. I am still a significant underdog even after Ed's poor roll, but that doesn't matter. The redouble is definitely correct. Ed took of course. I rolled 3-1. Not bad! I played B/24*, 4/1*. The position was now:
How would you feel in Ed's shoes? You have a 9-1 lead in the match, but you are sitting on an 8-cube with 2 men on the bar. You could lose the entire match this game. If Ed flunks, I have enough ammunition to continue with the attack. I also have enough time to scramble my back checker to the edge of the prime and over the blockade before my board cracks. Of course I will need the best of the luck, but winning a gammon and 16 points is definitely in sight. Considering where I was a roll ago behind 9-1 and my opponent being the clear favorite and holding a 2-cube, this is a pretty big improvement for me.
It would be nice to be able to report that all this happened. Unfortunately, it was not in the script. Ed rolled 3-1, I didn't roll too well from then on, and eventually I went down in flames. Still I had my chance, one I never should have gotten in the first place.
The moral here is that you have to be extra cautious when you have a big lead in the match and the cube starts flying. Before sending it over, you have to see how things will look not at the cube level you are turning it to, but at the level your opponent will be potentially turning it back to. If you do this, you will avoid the trap that Ed O'Laughlin fell into, which almost cost him a match which he was a big favorite to win.