I'll just consolidate some old quotes of mine here
Note the "long tail" on the chance of not finding a block after x time:
These two statements appear to be in dissonance, but are both true:
Obviously easy to confuse the two when calculating things.
So the chance a block won't be found after 10, 20 minutes, etc. (and the 1 in x chance)
20 13.53353% 7.39
30 4.97871% 20.09
40 1.83156% 54.60
50 0.67379% 148.41
60 0.24788% 403.43
70 0.09119% 1096.63
80 0.03355% 2980.96
90 0.01234% 8103.08
100 0.00454% 22026.47
110 0.00167% 59874.14
120 0.00061% 162754.79
130 0.00023% 442413.39
And after how many minutes will half of blocks, 25% of the blocks, etc. not be solved:
6.9314718056 50.00000% 2.00 (median block length)
13.8629436112 25.00000% 4.00
20.7944154168 12.50000% 8.00
27.7258872224 6.25000% 16.00
34.657359028 3.12500% 32.00
41.5888308336 1.56250% 64.00
And every day we can reasonably expect a block longer than 49 minutes, every week one longer than 69 minutes, every month 83 minutes:
49.6981329958 0.69444% 144.00
69.1572344863 0.09921% 1008.00
83.8548870042 0.02282% 4383.00
- The average time to solve a block is 10 minutes
- Half the blocks will be solved in under 7 minutes
Obviously easy to confuse the two when calculating things.
So the chance a block won't be found after 10, 20 minutes, etc. (and the 1 in x chance)
Code:
>>> for x in range(10,131,10) :
print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
10 36.78794% 2.72 (average block length)print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
20 13.53353% 7.39
30 4.97871% 20.09
40 1.83156% 54.60
50 0.67379% 148.41
60 0.24788% 403.43
70 0.09119% 1096.63
80 0.03355% 2980.96
90 0.01234% 8103.08
100 0.00454% 22026.47
110 0.00167% 59874.14
120 0.00061% 162754.79
130 0.00023% 442413.39
And after how many minutes will half of blocks, 25% of the blocks, etc. not be solved:
Code:
>>> for x in [ 10*math.log(2), 10*math.log(4), 10*math.log(8), 10*math.log(16), 10*math.log(32), 10*math.log(64)]:
print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
6.9314718056 50.00000% 2.00 (median block length)
13.8629436112 25.00000% 4.00
20.7944154168 12.50000% 8.00
27.7258872224 6.25000% 16.00
34.657359028 3.12500% 32.00
41.5888308336 1.56250% 64.00
And every day we can reasonably expect a block longer than 49 minutes, every week one longer than 69 minutes, every month 83 minutes:
Code:
>>> for x in [ 10*math.log(144), 10*math.log(144*7), 10*math.log(144*365.25/12)]:
print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
print x, '%2.5f%%' % (100*math.exp(-x/10)), '%1.2f' % (math.exp(x/10))
49.6981329958 0.69444% 144.00
69.1572344863 0.09921% 1008.00
83.8548870042 0.02282% 4383.00
Note the "long tail" on the chance of not finding a block after x time:
...the probability density function of an exponential distribution looks like this:
Note that the average block time is 10 minutes (1/λ), but 50% of the blocks are less than 6.93 minutes (the median ln(2)/λ).
Note that the average block time is 10 minutes (1/λ), but 50% of the blocks are less than 6.93 minutes (the median ln(2)/λ).
Most long blocks came early in Bitcoin, here's 212 blocks with over 100 minutes since last block timestamp.
Note that the block timestamp is based on the mining computer's time, there are more blocks than this with a negative time.
15324 1508.9
16564 1506.5
15 1452.6
16592 1229.7
20189 1003.4
19724 785.5
21438 637.0
19722 625.6
28 514.7
16490 511.4
20432 507.1
20364 500.2
20349 488.8
21389 468.7
19565 433.3
15048 422.9
19726 415.1
74638 411.3
21446 392.9
21527 384.7
21466 384.2
16468 380.7
26242 368.3
21359 357.8
21449 342.3
21463 330.1
21382 327.1
21376 321.3
21383 308.6
23418 305.4
21585 302.0
23434 300.7
20384 299.6
16215 294.8
15424 285.1
23433 277.6
21442 263.8
16286 263.8
21464 261.6
22945 260.1
22527 259.3
20325 248.2
21458 238.0
21374 234.9
19725 234.2
21418 232.2
21444 230.8
28705 226.3
21440 225.9
21348 225.1
1390 224.3
11964 223.8
169 222.4
21462 220.2
21403 217.6
21331 217.3
20435 216.1
8231 214.7
20439 211.4
1398 211.2
32647 208.9
13889 208.9
20190 205.3
16271 202.3
20187 198.4
21361 196.8
13898 196.4
1917 196.1
21340 195.0
25788 194.1
26237 191.6
20405 190.9
8211 190.7
20357 190.7
1296 188.3
21385 188.2
11966 186.9
32629 186.3
15228 186.1
21393 179.2
21459 178.8
20344 175.6
8226 175.2
20008 174.9
163 174.2
21428 172.7
20361 170.8
20343 170.4
18030 166.6
79 165.9
20339 163.7
23425 163.0
21380 162.4
20436 161.9
21584 161.5
20418 160.8
21345 160.1
25740 158.1
20417 157.4
20351 157.3
21581 156.5
21443 155.1
1916 155.1
20308 155.0
28742 154.3
16588 154.0
21447 150.8
20427 150.4
23426 148.7
22950 147.5
13082 146.9
21441 146.5
21332 146.5
15331 146.3
20390 145.0
155290 144.8
1389 143.5
149098 141.0
20310 140.0
20356 137.2
70718 135.9
21423 134.5
70665 133.2
20304 132.8
15818 132.8
21369 132.2
20333 132.0
20376 129.3
20188 128.7
17149 127.9
21325 127.5
20438 126.2
20421 124.4
22018 123.0
32527 122.1
25132 122.0
15222 121.8
69515 121.4
20203 121.3
76594 121.2
26275 121.0
20191 120.9
26236 120.6
105909 120.5
25889 120.3
28702 120.2
23421 120.1
156113 119.6
154185 119.4
19951 117.8
20411 116.4
21586 116.2
21360 115.9
16590 115.6
24419 115.4
16565 115.3
20359 115.3
26843 114.6
24956 114.4
163966 114.0
21323 113.4
26873 113.2
24415 112.8
24494 112.7
21422 112.5
23430 112.3
207497 112.2
26249 112.1
26201 112.0
26190 111.6
87107 111.2
175720 110.5
26212 110.1
20327 109.6
21451 109.5
18253 109.4
28731 108.2
21334 108.0
26104 107.5
8223 107.0
205771 106.5
22158 106.3
21461 106.2
32632 105.9
13892 105.7
21433 105.7
25130 105.5
206669 105.4
28697 105.3
152996 104.7
204798 104.4
20347 104.3
18265 104.3
25033 104.3
20334 104.2
20381 103.8
21408 103.5
28771 103.5
8227 103.1
26260 102.9
21597 102.3
154346 102.2
28749 102.1
19977 102.0
25117 101.9
24263 101.8
21373 101.5
26126 101.3
15230 101.0
25147 100.2
26251 100.1
Note that the block timestamp is based on the mining computer's time, there are more blocks than this with a negative time.
15324 1508.9
16564 1506.5
15 1452.6
16592 1229.7
20189 1003.4
19724 785.5
21438 637.0
19722 625.6
28 514.7
16490 511.4
20432 507.1
20364 500.2
20349 488.8
21389 468.7
19565 433.3
15048 422.9
19726 415.1
74638 411.3
21446 392.9
21527 384.7
21466 384.2
16468 380.7
26242 368.3
21359 357.8
21449 342.3
21463 330.1
21382 327.1
21376 321.3
21383 308.6
23418 305.4
21585 302.0
23434 300.7
20384 299.6
16215 294.8
15424 285.1
23433 277.6
21442 263.8
16286 263.8
21464 261.6
22945 260.1
22527 259.3
20325 248.2
21458 238.0
21374 234.9
19725 234.2
21418 232.2
21444 230.8
28705 226.3
21440 225.9
21348 225.1
1390 224.3
11964 223.8
169 222.4
21462 220.2
21403 217.6
21331 217.3
20435 216.1
8231 214.7
20439 211.4
1398 211.2
32647 208.9
13889 208.9
20190 205.3
16271 202.3
20187 198.4
21361 196.8
13898 196.4
1917 196.1
21340 195.0
25788 194.1
26237 191.6
20405 190.9
8211 190.7
20357 190.7
1296 188.3
21385 188.2
11966 186.9
32629 186.3
15228 186.1
21393 179.2
21459 178.8
20344 175.6
8226 175.2
20008 174.9
163 174.2
21428 172.7
20361 170.8
20343 170.4
18030 166.6
79 165.9
20339 163.7
23425 163.0
21380 162.4
20436 161.9
21584 161.5
20418 160.8
21345 160.1
25740 158.1
20417 157.4
20351 157.3
21581 156.5
21443 155.1
1916 155.1
20308 155.0
28742 154.3
16588 154.0
21447 150.8
20427 150.4
23426 148.7
22950 147.5
13082 146.9
21441 146.5
21332 146.5
15331 146.3
20390 145.0
155290 144.8
1389 143.5
149098 141.0
20310 140.0
20356 137.2
70718 135.9
21423 134.5
70665 133.2
20304 132.8
15818 132.8
21369 132.2
20333 132.0
20376 129.3
20188 128.7
17149 127.9
21325 127.5
20438 126.2
20421 124.4
22018 123.0
32527 122.1
25132 122.0
15222 121.8
69515 121.4
20203 121.3
76594 121.2
26275 121.0
20191 120.9
26236 120.6
105909 120.5
25889 120.3
28702 120.2
23421 120.1
156113 119.6
154185 119.4
19951 117.8
20411 116.4
21586 116.2
21360 115.9
16590 115.6
24419 115.4
16565 115.3
20359 115.3
26843 114.6
24956 114.4
163966 114.0
21323 113.4
26873 113.2
24415 112.8
24494 112.7
21422 112.5
23430 112.3
207497 112.2
26249 112.1
26201 112.0
26190 111.6
87107 111.2
175720 110.5
26212 110.1
20327 109.6
21451 109.5
18253 109.4
28731 108.2
21334 108.0
26104 107.5
8223 107.0
205771 106.5
22158 106.3
21461 106.2
32632 105.9
13892 105.7
21433 105.7
25130 105.5
206669 105.4
28697 105.3
152996 104.7
204798 104.4
20347 104.3
18265 104.3
25033 104.3
20334 104.2
20381 103.8
21408 103.5
28771 103.5
8227 103.1
26260 102.9
21597 102.3
154346 102.2
28749 102.1
19977 102.0
25117 101.9
24263 101.8
21373 101.5
26126 101.3
15230 101.0
25147 100.2
26251 100.1
Deepceleron's razor #17: If something is worth saying to a noob, deepceleron has probably already said it.