Some of the factors that affect whether to split are:
1. Relative board strength. If your opponent's board is stronger than yours, and he has enough material for a blitz (say, ten or even nine checkers), then you should be wary of splitting. Conversely, if you outboard your opponent, then you often don't need to be afraid of an attack even if he seems to have a lot of ammunition on hand.
2. Whether your opponent has an advanced anchor. If the positions look roughly equal except that your opponent has an advanced anchor while you are still stuck back on the ace point, then splitting is often necessary even if it looks dangerous. The danger of hanging back is that you will be slowly suffocated to death by a prime. You can't attack or counterprime your opponent's advanced anchor, so you're reduced to waiting for a shot from the ace point—a much gloomier prospect than playing a mutual holding game. Because getting a blot hit creates immediate pain, it is tempting to put off the day of judgment by refusing to split, but a slow death is no less inexorable than a quick one. Note that the flip side of this coin is that if the position is about even and you're both still on the ace point, then splitting to create an advanced anchor is often a powerful play because it puts pressure on your opponent to follow suit or fall behind.
3. The timing of your prime versus your opponent's. If both of you are stuck on the ace point then the timing of the priming game is likely to be a critical factor. Ask yourself what will happen if both of you stick to the priming plan. Who is likely to blink first? Typically, if you are behind in the race, you will want to hang back. The priming game is likely to go your way. On the other hand if you are ahead in the race then you should keep an eye out for a chance to get the back checkers moving.
In the position at hand, point #2 (the advanced anchor) does not apply. White is slightly ahead in the race, with a stronger board and a more advanced prime. These suggest that splitting is an option to be considered seriously. Of course if White had rolled something that could be used to significantly improved his prime, like 6-2 or 6-3 or even 2-1, then continuing to build the prime is probably the right option, since White is not in immediate danger of being locked in right now. However, 3-2 is not a good roll for prime-building here, so I would split.
How to split is another question. Blue's potential attack is threatening enough that I would be inclined to make the safest split, 24/22 9/6, but I'm not sure it's right since 9/6 is so awkward. 24/22 13/10 is possible but does leave a lot of blots that could spell trouble.
One final remark, about "coming under the gun." Sometimes one hears the rule of thumb that coming within direct-shot range of three attackers is very dangerous and should discourage you from splitting. While it is good to be cognizant of how many attacking rolls your opponent has, I've found that the three factors I've listed above tend to be more important considerations than simply checking whether you're coming under the gun. As an example, see the position below, which I misplayed OTB because I was afraid to come under the gun. But my opponent has an advanced anchor and board strength is equal, so splitting is definitely called for.
Unlimited game: tchow to play 42
| gnubg | 143 |
|---|---|
| |
| tchow | 153 |
Position ID: cG/CAQaw58EBMA Match ID: cAkKAAAAAAAA | |
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| • | 1 | R | 24/22 6/2 | -0.610 | ||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 869399626 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 2 | R | 24/22 13/9 | -0.706 ( -0.096) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 869399626 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 3 | R | 8/2 | -0.755 ( -0.144) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 869399626 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| 4 | R | 13/7 | -0.763 ( -0.153) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 869399626 and quasi-random dice | ||||||||||||||||||||||
| Play: supremo 2-ply cubeful prune [world class] | ||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 | ||||||||||||||||||||||
| Skip pruning for 1-ply moves. | ||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | ||||||||||||||||||||||