dammit…missed your bit about the bishops…
let’s revise…
16 bishop positions that satisfy your clause
6 king possibilities
5 queen possibilities
6 knight possibilities
1 rook combo
166561 = 2880
Which means, you are correct!
My bad…
Seeing so many 445 and doubting the complete accuracy of my own count, I actually transcribed all the moves possible. And yes, Virginia, there are 445 first-two-moves combinations (not counting possible captures). They are:
Move First Second
==== ===== ======
1 Pa2a3 Pa3a4
2 Pa2a3 Pb2b3
3 Pa2a3 Pb2b4
4 Pa2a3 Pc2c3
5 Pa2a3 Pc2c4
6 Pa2a3 Pd2d3
7 Pa2a3 Pd2d4
8 Pa2a3 Pe2e3
9 Pa2a3 Pe2e4
10 Pa2a3 Pf2f3
11 Pa2a3 Pf2f4
12 Pa2a3 Pg2g3
13 Pa2a3 Pg2g4
14 Pa2a3 Ph2h3
15 Pa2a3 Ph2h4
16 Pa2a3 Nb1c3
17 Pa2a3 Ng1f3
18 Pa2a3 Ng1h3
19 Pa2a3 Ra1a2
20 Pb2b3 Pa2a3
21 Pb2b3 Pa2a4
22 Pb2b3 Pb3b4
23 Pb2b3 Pc2c3
24 Pb2b3 Pc2c4
25 Pb2b3 Pd2d3
26 Pb2b3 Pd2d4
27 Pb2b3 Pe2e3
28 Pb2b3 Pe2e4
29 Pb2b3 Pf2f3
30 Pb2b3 Pf2f4
31 Pb2b3 Pg2g3
32 Pb2b3 Pg2g4
33 Pb2b3 Ph2h3
34 Pb2b3 Ph2h4
35 Pb2b3 Nb1a3
36 Pb2b3 Nb1c3
37 Pb2b3 Ng1f3
38 Pb2b3 Ng1h3
39 Pb2b3 Bc1b2
40 Pb2b3 Bc1a3
41 Pc2c3 Pa2a3
42 Pc2c3 Pa2a4
43 Pc2c3 Pb2b3
44 Pc2c3 Pb2b4
45 Pc2c3 Pc3c4
46 Pc2c3 Pd2d3
47 Pc2c3 Pd2d4
48 Pc2c3 Pe2e3
49 Pc2c3 Pe2e4
50 Pc2c3 Pf2f3
51 Pc2c3 Pf2f4
52 Pc2c3 Pg2g3
53 Pc2c3 Pg2g4
54 Pc2c3 Ph2h3
55 Pc2c3 Ph2h4
56 Pc2c3 Nb1a3
57 Pc2c3 Ng1f3
58 Pc2c3 Ng1h3
59 Pc2c3 Kd1c2
60 Pd2d3 Pa2a3
61 Pd2d3 Pa2a4
62 Pd2d3 Pb2b3
63 Pd2d3 Pb2b4
64 Pd2d3 Pc2c3
65 Pd2d3 Pc2c4
66 Pd2d3 Pd3d4
67 Pd2d3 Pe2e3
68 Pd2d3 Pe2e4
69 Pd2d3 Pf2f3
70 Pd2d3 Pf2f4
71 Pd2d3 Pg2g3
72 Pd2d3 Pg2g4
73 Pd2d3 Ph2h3
74 Pd2d3 Ph2h4
75 Pd2d3 Nb1a3
76 Pd2d3 Nb1c3
77 Pd2d3 Nb1d2
78 Pd2d3 Ng1f3
79 Pd2d3 Ng1h3
80 Pd2d3 Kd1d2
81 Pd2d3 Qe1d2
82 Pd2d3 Qe1c3
83 Pd2d3 Qe1b4
84 Pd2d3 Qe1a5
85 Pd2d3 Bc1d2
86 Pd2d3 Bc1e3
87 Pd2d3 Bc1f4
88 Pd2d3 Bc1g5
89 Pd2d3 Bc1h6
90 Pe2e3 Pa2a3
91 Pe2e3 Pa2a4
92 Pe2e3 Pb2b3
93 Pe2e3 Pb2b4
94 Pe2e3 Pc2c3
95 Pe2e3 Pc2c4
96 Pe2e3 Pd2d3
97 Pe2e3 Pd2d4
98 Pe2e3 Pe3e4
99 Pe2e3 Pf2f3
100 Pe2e3 Pf2f4
101 Pe2e3 Pg2g3
102 Pe2e3 Pg2g4
103 Pe2e3 Ph2h3
104 Pe2e3 Ph2h4
105 Pe2e3 Nb1a3
106 Pe2e3 Nb1c3
107 Pe2e3 Ng1e2
108 Pe2e3 Ng1f3
109 Pe2e3 Ng1h3
110 Pe2e3 Kd1e2
111 Pe2e3 Qe1e2
112 Pe2e3 Bf1e2
113 Pe2e3 Bf1d3
114 Pe2e3 Bf1c4
115 Pe2e3 Bf1b5
116 Pe2e3 Bf1a6
117 Pf2f3 Pa2a3
118 Pf2f3 Pa2a4
119 Pf2f3 Pb2b3
120 Pf2f3 Pb2b4
121 Pf2f3 Pc2c3
122 Pf2f3 Pc2c4
123 Pf2f3 Pd2d3
124 Pf2f3 Pd2d4
125 Pf2f3 Pe2e3
126 Pf2f3 Pe2e4
127 Pf2f3 Pf3f4
128 Pf2f3 Pg2g3
129 Pf2f3 Pg2g4
130 Pf2f3 Ph2h3
131 Pf2f3 Ph2h4
132 Pf2f3 Nb1a3
133 Pf2f3 Nb1c3
134 Pf2f3 Ng1h3
135 Pf2f3 Qe1f2
136 Pf2f3 Qe1g3
137 Pf2f3 Qe1h4
138 Pg2g3 Pa2a3
139 Pg2g3 Pa2a4
140 Pg2g3 Pb2b3
141 Pg2g3 Pb2b4
142 Pg2g3 Pc2c3
143 Pg2g3 Pc2c4
144 Pg2g3 Pd2d3
145 Pg2g3 Pd2d4
146 Pg2g3 Pe2e3
147 Pg2g3 Pe2e4
148 Pg2g3 Pf2f3
149 Pg2g3 Pf2f4
150 Pg2g3 Pg3g4
151 Pg2g3 Ph2h3
152 Pg2g3 Ph2h4
153 Pg2g3 Nb1a3
154 Pg2g3 Nb1c3
155 Pg2g3 Ng1f3
156 Pg2g3 Ng1h3
157 Pg2g3 Bf1g2
158 Pg2g3 Bf1h3
159 Ph2h3 Pa2a3
160 Ph2h3 Pa2a4
161 Ph2h3 Pb2b3
162 Ph2h3 Pb2b4
163 Ph2h3 Pc2c3
164 Ph2h3 Pc2c4
165 Ph2h3 Pd2d3
166 Ph2h3 Pd2d4
167 Ph2h3 Pe2e3
168 Ph2h3 Pe2e4
169 Ph2h3 Pf2f3
170 Ph2h3 Pf2f4
171 Ph2h3 Pg2g3
172 Ph2h3 Pg2g4
173 Ph2h3 Ph3h4
174 Ph2h3 Nb1a3
175 Ph2h3 Nb1c3
176 Ph2h3 Ng1f3
177 Ph2h3 Rh1h2
178 Pa2a4 Pa4a5
179 Pa2a4 Pb2b3
180 Pa2a4 Pb2b4
181 Pa2a4 Pc2c3
182 Pa2a4 Pc2c4
183 Pa2a4 Pd2d3
184 Pa2a4 Pd2d4
185 Pa2a4 Pe2e3
186 Pa2a4 Pe2e4
187 Pa2a4 Pf2f3
188 Pa2a4 Pf2f4
189 Pa2a4 Pg2g3
190 Pa2a4 Pg2g4
191 Pa2a4 Ph2h3
192 Pa2a4 Ph2h4
193 Pa2a4 Nb1a3
194 Pa2a4 Nb1c3
195 Pa2a4 Ng1f3
196 Pa2a4 Ng1h3
197 Pa2a4 Ra1a2
198 Pa2a4 Ra1a3
199 Pb2b4 Pa2a3
200 Pb2b4 Pa2a4
201 Pb2b4 Pb4b5
202 Pb2b4 Pc2c3
203 Pb2b4 Pc2c4
204 Pb2b4 Pd2d3
205 Pb2b4 Pd2d4
206 Pb2b4 Pe2e3
207 Pb2b4 Pe2e4
208 Pb2b4 Pf2f3
209 Pb2b4 Pf2f4
210 Pb2b4 Pg2g3
211 Pb2b4 Pg2g4
212 Pb2b4 Ph2h3
213 Pb2b4 Ph2h4
214 Pb2b4 Nb1a3
215 Pb2b4 Nb1c3
216 Pb2b4 Ng1f3
217 Pb2b4 Ng1h3
218 Pb2b4 Bc1b2
219 Pb2b4 Bc1a3
220 Pc2c4 Pa2a3
221 Pc2c4 Pa2a4
222 Pc2c4 Pb2b3
223 Pc2c4 Pb2b4
224 Pc2c4 Pc4c5
225 Pc2c4 Pd2d3
226 Pc2c4 Pd2d4
227 Pc2c4 Pe2e3
228 Pc2c4 Pe2e4
229 Pc2c4 Pf2f3
230 Pc2c4 Pf2f4
231 Pc2c4 Pg2g3
232 Pc2c4 Pg2g4
233 Pc2c4 Ph2h3
234 Pc2c4 Ph2h4
235 Pc2c4 Nb1a3
236 Pc2c4 Nb1c3
237 Pc2c4 Ng1f3
238 Pc2c4 Ng1h3
239 Pc2c4 Kd1c2
240 Pd2d4 Pa2a3
241 Pd2d4 Pa2a4
242 Pd2d4 Pb2b3
243 Pd2d4 Pb2b4
244 Pd2d4 Pc2c3
245 Pd2d4 Pc2c4
246 Pd2d4 Pd4d5
247 Pd2d4 Pe2e3
248 Pd2d4 Pe2e4
249 Pd2d4 Pf2f3
250 Pd2d4 Pf2f4
251 Pd2d4 Pg2g3
252 Pd2d4 Pg2g4
253 Pd2d4 Ph2h3
254 Pd2d4 Ph2h4
255 Pd2d4 Nb1a3
256 Pd2d4 Nb1c3
257 Pd2d4 Nb1d2
258 Pd2d4 Ng1f3
259 Pd2d4 Ng1h3
260 Pd2d4 Kd1d2
261 Pd2d4 Qe1d2
262 Pd2d4 Qe1c3
263 Pd2d4 Qe1b4
264 Pd2d4 Qe1a5
265 Pd2d4 Bc1d2
266 Pd2d4 Bc1e3
267 Pd2d4 Bc1f4
268 Pd2d4 Bc1g5
269 Pd2d4 Bc1h6
270 Pe2e4 Pa2a3
271 Pe2e4 Pa2a4
272 Pe2e4 Pb2b3
273 Pe2e4 Pb2b4
274 Pe2e4 Pc2c3
275 Pe2e4 Pc2c4
276 Pe2e4 Pd2d3
277 Pe2e4 Pd2d4
278 Pe2e4 Pe4e5
279 Pe2e4 Pf2f3
280 Pe2e4 Pf2f4
281 Pe2e4 Pg2g3
282 Pe2e4 Pg2g4
283 Pe2e4 Ph2h3
284 Pe2e4 Ph2h4
285 Pe2e4 Nb1a3
286 Pe2e4 Nb1c3
287 Pe2e4 Ng1e2
288 Pe2e4 Ng1f3
289 Pe2e4 Ng1h3
290 Pe2e4 Kd1e2
291 Pe2e4 Qe1e2
292 Pe2e4 Qe1e3
293 Pe2e4 Bf1e2
294 Pe2e4 Bf1d3
295 Pe2e4 Bf1c4
296 Pe2e4 Bf1b5
297 Pe2e4 Bf1a6
298 Pf2f4 Pa2a3
299 Pf2f4 Pa2a4
300 Pf2f4 Pb2b3
301 Pf2f4 Pb2b4
302 Pf2f4 Pc2c3
303 Pf2f4 Pc2c4
304 Pf2f4 Pd2d3
305 Pf2f4 Pd2d4
306 Pf2f4 Pe2e3
307 Pf2f4 Pe2e4
308 Pf2f4 Pf4f5
309 Pf2f4 Pg2g3
310 Pf2f4 Pg2g4
311 Pf2f4 Ph2h3
312 Pf2f4 Ph2h4
313 Pf2f4 Nb1a3
314 Pf2f4 Nb1c3
315 Pf2f4 Ng1f3
316 Pf2f4 Ng1h3
317 Pf2f4 Qe1f2
318 Pf2f4 Qe1g3
319 Pf2f4 Qe1h4
320 Pg2g4 Pa2a3
321 Pg2g4 Pa2a4
322 Pg2g4 Pb2b3
323 Pg2g4 Pb2b4
324 Pg2g4 Pc2c3
325 Pg2g4 Pc2c4
326 Pg2g4 Pd2d3
327 Pg2g4 Pd2d4
328 Pg2g4 Pe2e3
329 Pg2g4 Pe2e4
330 Pg2g4 Pf2f3
331 Pg2g4 Pf2f4
332 Pg2g4 Pg3g4
333 Pg2g4 Ph2h3
334 Pg2g4 Ph2h4
335 Pg2g4 Nb1a3
336 Pg2g4 Nb1c3
337 Pg2g4 Ng1f3
338 Pg2g4 Ng1h3
339 Pg2g4 Bf1g2
340 Pg2g4 Bf1h3
341 Ph2h4 Pa2a3
342 Ph2h4 Pa2a4
343 Ph2h4 Pb2b3
344 Ph2h4 Pb2b4
345 Ph2h4 Pc2c3
346 Ph2h4 Pc2c4
347 Ph2h4 Pd2d3
348 Ph2h4 Pd2d4
349 Ph2h4 Pe2e3
350 Ph2h4 Pe2e4
351 Ph2h4 Pf2f3
352 Ph2h4 Pf2f4
353 Ph2h4 Pg2g3
354 Ph2h4 Pg2g4
355 Ph2h4 Ph4h5
356 Ph2h4 Nb1a3
357 Ph2h4 Nb1c3
358 Ph2h4 Ng1f3
359 Ph2h4 Ng1h3
360 Ph2h4 Rh1h2
361 Ph2h4 Rh1h3
362 Nb1a3 Na3b5
363 Nb1a3 Na3c4
364 Nb1a3 Na3b1
365 Nb1a3 Ng1f3
366 Nb1a3 Ng1h3
367 Nb1a3 Pb2b3
368 Nb1a3 Pb2b4
369 Nb1a3 Pc2c3
370 Nb1a3 Pc2c4
371 Nb1a3 Pd2d3
372 Nb1a3 Pd2d4
373 Nb1a3 Pe2e3
374 Nb1a3 Pe2e4
375 Nb1a3 Pf2f3
376 Nb1a3 Pf2f4
377 Nb1a3 Pg2g3
378 Nb1a3 Pg2g4
379 Nb1a3 Ph2h3
380 Nb1a3 Ph2h4
381 Nb1a3 Ra1b1
382 Nb1c3 Nc3b1
383 Nb1c3 Nc3a4
384 Nb1c3 Nc3b5
385 Nb1c3 Nc3d5
386 Nb1c3 Nc3e4
387 Nb1c3 Ng1f3
388 Nb1c3 Ng1h3
389 Nb1c3 Pa2a3
390 Nb1c3 Pa2a4
391 Nb1c3 Pb2b3
392 Nb1c3 Pb2b4
393 Nb1c3 Pd2d3
394 Nb1c3 Pd2d4
395 Nb1c3 Pe2e3
396 Nb1c3 Pe2e4
397 Nb1c3 Pf2f3
398 Nb1c3 Pf2f4
399 Nb1c3 Pg2g3
400 Nb1c3 Pg2g4
401 Nb1c3 Ph2h3
402 Nb1c3 Ph2h4
403 Nb1c3 Ra1b1
404 Ng1f3 Nf3d4
405 Ng1f3 Nf3e5
406 Ng1f3 Nf3g5
407 Ng1f3 Nf3h4
408 Ng1f3 Nf3g1
409 Ng1f3 Nb1a3
410 Ng1f3 Nb1c3
411 Ng1f3 Pa2a3
412 Ng1f3 Pa2a4
413 Ng1f3 Pb2b3
414 Ng1f3 Pb2b4
415 Ng1f3 Pc2c3
416 Ng1f3 Pc2c4
417 Ng1f3 Pd2d3
418 Ng1f3 Pd2d4
419 Ng1f3 Pe2e3
420 Ng1f3 Pe2e4
421 Ng1f3 Pg2g3
422 Ng1f3 Pg2g4
423 Ng1f3 Ph2h3
424 Ng1f3 Ph2h4
425 Ng1f3 Rh1g1
426 Ng1h3 Nh3g5
427 Ng1h3 Nh3f4
428 Ng1h3 Nh3g1
429 Ng1h3 Nb1a3
430 Ng1h3 Nb1c3
431 Ng1h3 Pa2a3
432 Ng1h3 Pa2a4
433 Ng1h3 Pb2b3
434 Ng1h3 Pb2b4
435 Ng1h3 Pc2c3
436 Ng1h3 Pc2c4
437 Ng1h3 Pd2d3
438 Ng1h3 Pd2d4
439 Ng1h3 Pe2e3
440 Ng1h3 Pe2e4
441 Ng1h3 Pf2f3
442 Ng1h3 Pf2f4
443 Ng1h3 Pg2g3
444 Ng1h3 Pg2g4
445 Ng1h3 Rh1g1
After that last tour de force by AWB, I have to agree with the above! 
I think I follow all of this except one small point. Discounting captures. Why discount captures?
Just who is this wizard of the sixty-four square madhouse that you are playing where you have to discount his captures? In order to affect your arithmetic the black piece must capture white’s piece on his first move! No one is that good.
There are a limited number of black’s first move positions which leave you options to capture. These should be added to your total. Fourteen of black’s first moves after eight specific first pawn moves by white allow white to make second move pawn captures, plus the six variations which allow you captures on your second knight moves, (thus being different positions). Twenty additional first two moves by white.
Tris
I can understand the captures by pawns, since that results in piece movements different than what we’ve already reviewed.
But the moves that include captures by knights have already been accounted for–in your case they capture a pawn, but the two moves are the same. Also, why add captures by knights, but not by bishops? And is a bishop capturing a pawn different than it capturing a knight? (Although I wouldn’t count captures by bishops either–these moves have also already been accounted for)
Confused in Cary.
Great list, AWB! Thanks!
Tris, I think the conditions were set forth in the OP, i.e., White making two consecutive moves.
Interestingly, there is a story about Paul Morphy, the first American world champion, who was willing to give almost any odds to almost anyone. He would take his queen off the board and play against the strongest players in the world. But once, a patzer wanted to play him, but instead of any sort of material odds, he wanted something else. “Keep all your pieces,” he told Morphy, “but let me have two consecutive moves at any one time of my choice.”
Morphy instantly and adamantly refused.
Let’s find out.
One…
A-two-hoo…
Three…
<CRUNCH>
… three.
Yeah, you’re right. I forgot about the bishops entirely. and one queen move, too. OK, those moves are accounted for, and the difference in chess position are not being considered. So, there are only the 14 new moves to be added.
Libertarian said:
I’ll be charitable and say I find this statement exaggerated.
Morphy at the height of his powers could probably have given pawn and move to any other top master and still prevailed in a match; indeed, he did just that against Owen, in 1856 I think. But to imagine Morphy could routinely give Q odds overstates not only his abilities, fabulous as they were, but denigrates the talents of other players. A rough equivalent would be to suggest Tiger Woods could beat the Singhs and Duvals of the world using only his driver and putter.
It’s true Morphy played many games at odds. Here he wins at age 12 giving rook odds. Often he played without his queen knight. But these were casual games against vastly inferior players, easy going encounters over drinks and cigars, not nerve wracking encounters with the world’s best.
Wow! Thanks all. Now the next time I “count sheep” I’ll know where to stop. 
And I’ll sleep soundly knowing that if chess games are played for the next hundred thousand years, mankind will never come close to exhausting all the possibilities. 25 X 10[sup]115[/sup]. Wow.
-b
I’ll second this statement. Morphy couldn’t give queen’s odds against the best players in his day and win consistently.
Personally, I’m not even rated, have played in one tournament in 7th grade, am extremely out of practice, and yet I don’t believe there’s a player on earth who could give me queens odds every game and beat me in a match. (I’d look to trade pieces at every opportunity and win by attrition)
So…how come we can get so many responses to a thread like this, yet every SDMB group chess thread dies a quick yet ignoble death? 
Because, darn it, we need chess cheerleaders!
“Queen that pawn! Queen that pawn! Yaaaaaaaay white!!”