A bogey number is a score than can not be taken out in the same number of darts that a higher score can be taken out.
Everyone knows the bogey numbers, right? 169, 168, 166, 165, 163, 162, 159
170 is the highest score that can be taken out in three darts while lower scores 169, 168, 166, 165, 163, 162, and 159 can not. We learn these numbers so we can give ourselves the opportunity to land on the higher number that gives us a chance to win the leg in the fewest number of darts rather than the lower number that will require an additional visit to the oche.
If you have one dart in hand and a score of 186, it would be a mistake to throw at treble 20, as a single 20 would leave you on a bogey 166 that you won’t be able to finish on your next round. Better to throw at treble 19 and let the single leave you on 167, which you can take out in style on your next visit.
Tip: If you have 220 left after two darts and the treble 20 is blocked, don’t switch to a different treble – they’ll all leave you on a bogey number. Instead, throw a double bull to leave 170.
Score with 1 dart in hand  Throw at  Leave 
195  25  170 
192  25  167 
189  19 (T19)  170 (132) 
188  18 (T18)  170 (134) 
186  19 (T19)  167 (129) 
185  18 (T18)  167 (131) 
183  19 (T19)  164 (126) 
182  18 (T18)  164 (128) 
179  19 (T19)  160 (122) 
But those seven are not the only bogey numbers. There are actually 77 numbers that can be considered a bogey, depending on how many darts you have in hand.
You probably know not to throw at the treble 20 when you start a round with a score of 119 – a single 20 will leave you on 99, which can’t be taken out with two darts. That makes 99 a two dart bogey number. If we follow our rule that a bogey is any score that can’t be taken out in the same number of darts as a higher score, we see that because 110 can be taken out in two darts, 109, 108, 106, 105, 103, 102, and 99 are all two dart bogey numbers.
Extending this to one dart, since 50 is the highest one dart out, everything below 50 that can’t be taken out in one dart is a bogey: 49, 48, 47, 46, 45, 44, 43, 42, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3.
I’m sure you were already aware of these bogey numbers, even if you didn’t necessarily call them that. But wait, there are more!
If 170 is the highest score that can be taken out in three darts, what’s the highest score that can be taken out in four darts? That would be 230 (170 plus another treble 20). So anything less than 230 that can’t be finished in four darts is also a bogey. These are the four dart bogey numbers: 229, 228, 226, 225, 223, 222, 219. How do you use this information? Just like the example above with a score of 186 and one dart in hand, if you have two darts in hand and a score exactly 20 point higher than any of these bogey number, don’t throw at treble 20, because the single 20 will leave you on a bogey number. Simple, right?
Score with 2 darts in hand  Throw at  Leave 
249  19 (T19)  230 (192) 
248  18 (T18)  230 (194) 
246  19 (T19)  227 (189) 
245  18 (T18)  227 (191) 
243  19 (T19)  224 (186) 
242  18 (T18)  224 (188) 
239  19 (T19)  220 (182) 
As you can see, each additional dart available increases the bogey numbers by 60. Since 290 can be finished in five darts and 289 can not, that makes 289 a five dart bogey number. Because you can take out 350 in six darts but not 345, 345 is a six dart bogey number.
Here are all 77 bogey numbers:
1 dart bogey numbers: 49, 48, 47, 46, 45, 44, 43, 42, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3 

2 dart bogey numbers: 109, 108, 106, 105, 103, 102, 99 

3 dart bogey numbers: 169, 168, 166, 165, 163, 162, 159 

4 dart bogey numbers (1 dart in hand): 229, 228, 226, 225, 223, 222, 219 

5 dart bogey numbers (2 darts in hand): 289, 288, 286, 285, 283, 282, 279 

6 dart bogey numbers (3 darts in hand): 349, 348, 346, 345, 343, 342, 339 

7 dart bogey numbers (1 dart in hand): 409, 408, 406, 405, 403, 402, 399 

8 dart bogey numbers (2 darts in hand): 469, 468, 466, 465, 463, 462, 459 
So, am I really saying you shouldn’t throw at treble 20 with one dart in hand and 369 remaining? I am. Throw at treble 19. If you hit treble 20 you return to 309. If you hit treble 19 you return to 312. (I think 312 is a better number anyway, but either way it will take you at least six more darts to finish.) If, however, you hit a single 20 you will return to a score of 349, which can’t be taken out in two visits. Hitting a single 19 with that last dart has you returning to 350 which can be taken out with rounds of 180 and 170. Are you going to hit it? Probably not. But the chance of you taking out 349 with six darts is exactly zero. Leave yourself the possibility of something great happening.
As for the higher bogey numbers, I include them mostly for completeness. I had to work to find a situation where you could land on one. Ready? Your first visit you throw a single 20 and two single ones, leaving 479. (Don’t pretend you’ve never done this.) The first dart of your next turn is a single 20 leaving you on 459, which is an 8 dart bogey. What does that mean? It means you’ve just blown your chance at a 12 darter – you can’t take out 459 with 8 darts. That first dart should have been thrown at 19’s where a single 19 would have left 460, which can be taken out with seven treble 20’s and a double 20.
I know it seems absurd to be worrying about a 12 darter after opening with a 22, but whenever you land on a bogey number, you’re giving your opponent three more darts to beat you. You may think that with 459 and two darts in hand you can just work your way down and ‘fix it later’. You can’t. Once you’re on a bogey number, you can throw big treble after big treble and you’ll still be on a bogey number. Throw five treble 20’s from here and you’ll have 159 with three darts in hand. Bogey number. The 12 darter was gone the moment you hit the single 20.
These higher bogey numbers are pretty much irrelevant if you’re not a world class player. Your scoring average will dictate that you’ll be giving your opponent quite a few more than three extra darts over the course of a leg (and he’ll be probably giving them right back to you), but as you get closer to a checkout (or become a better darter!), landing on a bogey number will cost you a leg that you could have won. So don’t do it. Avoid even the highest bogey numbers and give yourself the chance to win in the fewest darts possible.