The following table represents the approximate probabilities of encountering other ships in deep space away from the human bubble given their number in the galaxy.
The table assumes random distribution and does not take popular destinations such as the nebulae and the galactic core into account. It also does not take the time of exploration into account, but rather represents the probabilities of being in an encounter in a given moment. The table can be used to estimate both the chance of an encounter with another explorer, or the chance of encountering ship wrecks depending on what you assume the first column represents (either the number of other explorers, or the number of wrecked ships randomly spread across the galaxy). An encounter means that two or more ships are present in the same star system at a given moment, regardless of whether they detect each other (not being in super-cruise at the same time despite being in the same system further reduces the odds of actually registering other ships)
The table does not represent the probabilities of an encounter as is in the game, but as would be expected as according to the math, given the stated assumptions.
The numbers were calculated using WolframAlpha and using the same principles as for a birthday paradox as described here for the third column. For this problem, the math was simply adjusted by replacing the number of days in a year with the number of star systems in a galaxy, and by replacing the number of people comparing their birthday by a number of explorers comparing their current star system.
Example of a calculation for 1.000.000 ships: column 2, column 3
Results are rounded to two significant digits.
For obvious reasons, WolframAlpha refuses to commence with calculations involving combinatorics with large numbers. Because of this, a simplified equation (also available on the site explaining the birthday paradox) was used. Consequently, the calculations for the third column should contain error bars. However, it turns out that the errors are completely insignificant for all the relevant cases. Example of error-bar calculation for 1.000.000 ships.
* 99,99999999999999999999999999999999999999999999999999995%
The table assumes random distribution and does not take popular destinations such as the nebulae and the galactic core into account. It also does not take the time of exploration into account, but rather represents the probabilities of being in an encounter in a given moment. The table can be used to estimate both the chance of an encounter with another explorer, or the chance of encountering ship wrecks depending on what you assume the first column represents (either the number of other explorers, or the number of wrecked ships randomly spread across the galaxy). An encounter means that two or more ships are present in the same star system at a given moment, regardless of whether they detect each other (not being in super-cruise at the same time despite being in the same system further reduces the odds of actually registering other ships)
The table does not represent the probabilities of an encounter as is in the game, but as would be expected as according to the math, given the stated assumptions.
The numbers were calculated using WolframAlpha and using the same principles as for a birthday paradox as described here for the third column. For this problem, the math was simply adjusted by replacing the number of days in a year with the number of star systems in a galaxy, and by replacing the number of people comparing their birthday by a number of explorers comparing their current star system.
Example of a calculation for 1.000.000 ships: column 2, column 3
Results are rounded to two significant digits.
For obvious reasons, WolframAlpha refuses to commence with calculations involving combinatorics with large numbers. Because of this, a simplified equation (also available on the site explaining the birthday paradox) was used. Consequently, the calculations for the third column should contain error bars. However, it turns out that the errors are completely insignificant for all the relevant cases. Example of error-bar calculation for 1.000.000 ships.
| number of concurrent explorers | approximate probability of encountering at least one other ship in the system at a given moment | approximate probability of an encounter between at least two unspecified ships at a given moment |
| 100 | 1 : 4.000.000.000 | 1 : 81.000.000 |
| 1.000 | 1 : 400.000.000 | 1 : 800.000 |
| 10.000 | 1 : 40.000.000 | 1 : 8.000 |
| 100.000 | 1 : 4.000.000 | 1 : 81 or 1,2% |
| 750.000 | 1 : 530.000 | 1 : 2 or 50% |
| 1.000.000 | 1 : 400.000 | 71% |
| 1.900.000 | 1 : 210.000 | 99% |
| 10.000.000 | 1 : 40.000 | 100%* |
| 100.000.000 | 1 : 4.000 | 100% |
| 1.000.000.000 | 1 : 400 | 100% |
| 10.000.000.000 | 1 : 40 or 2,5% | 100% |
| 100.000.000.000 | 1 : 5 or 22% | 100% |
| 280.000.000.000 | 1 : 2 or 50% | 100% |
| 400.000.000.000 | 63% | 100% |
| number of ship wrecks across the galaxy | approximate probability of encountering at least one ship wreck in the system | approximate probability of at least two ship wrecks being in the same systems |
* 99,99999999999999999999999999999999999999999999999999995%
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