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BGonline.org Forums
framework
Posted By: David Rockwell In Response To: Screwing up another TG or cash situation (adambulldog)
Date: Monday, 6 April 2009, at 2:35 p.m.
I suck at TG problems. So, I will respond to the framework question rather than the position which is more difficult.
When you play on as TG, you have the chance to double again on the next turn. So, the framework needs to cover this period of time. Here is a concise description of the theory. There are 1296 two roll sequences. Divide these up into three categories.
1. too good after the next two shakes.
2. Not too good – double out
3. Not too good – take (whether a proper double can be given or not.)
On sequence #1, you have gained by your decision to play on. If your GNU equity is 1.1, your gain from playing on is 0.1 since you would have gotten 1.0 with a double out. This represents your future gammons when you play on.
On sequence #2, you have a wash with the immediate decision to double out. You could have gotten 1.0 with an earlier double out and you get 1.0 with a double out now. There is no gain or loss. Ignore these sequences.
On sequence #3, you have a loss from your decision to play on. If your GNU equity is 0.95, your loss is 0.05 since you could have gotten 1.0 with a double out.
When gains exceed losses, you are too good – play on.
This framework tells you what you need to see OTB. In Neil’s position, ask yourself how many gammons are you going to get (sequence #1) when you play on. Certainly when you hit the blot in the outfield, there will be some. Size up this opportunity to the best of your ability.
The key in my mind is sequence #3. Visualize what will be required to give your opponent a proper take next turn. In the position in question, I don’t know the answer to this question. That’s why I didn’t respond to Neil’s post. Let’s assume white needs to be at the edge of the prime after blue misses the shot in order to take. You need to size up how often this happens as well as how much value is in the take after one of these sequences. If instead, white can still not take a double after making this much progress, blue has little to lose by rolling. The position would then be clearly TG since sequence #3 is near zero.
I certainly do not recommend that anyone do any math to solve these problems OTB. However, trying to imagine the take point can be very helpful. It’s a lot better than guessing.
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