When a shared birthday becomes likely

• the near-birthday chance at k = 0 is a distinct-birthday chance on a shorter year ×7
• 4 lists find solutions at 12 bits in most runs ×4
• at the predicted sample size the measured typical error is near a tenth for 1000 ×3
• 22 is still under a half ×1
• 23 is over it ×1
• a block is between 2 and 365 days ×1
• a few thousand draws pin ten thousand kinds to within several per cent ×1
• a group smaller than the calendar ×1
• a larger first sample lets the smoothed sum reach further ×1
• a match within a day needs 14 ×1
• a run with a solution is found among the first fifty ×1
• a seasonal swing is between nothing and the whole mean ×1
• a spike holds more than its fair share and less than everything ×1
• a tail and a cycle short enough to draw ×1
• a weekend day is thinned, not removed or boosted ×1
• an exact match needs 23 people ×1
• an uneven calendar has at most as many effective days as it has days ×1
• and its mean length is within ten per cent of √(πp/2) ×1
• and no calendar needs a bigger room than the even year ×1
• and the four cancel ×1
• and the threshold only falls ×1
• and where it misses, the calendar needs one MORE person than its effective days predict, never one fewer ×1
• at 512 strings a list, four lists nearly always succeed and two nearly never do ×1
• at t = 1 the plain estimate is within ten per cent ×1
• at t = 1.5 the spread is more than ten billion times the answer ×1
• at t = 2 the smoothed mean is within ten per cent ×1
• at t = 6 the smoothed sum falls short of the truth ×1
• at the last step the two agree modulo the factor found ×1
• averaged over two hundred samples the sum is within two per cent of the truth for t ≤ 1 ×1
• before the last step they agree modulo neither prime ×1
• between 4 and 24 slots, every one possible ×1
• c = 0 and c = −2 run far longer ×1
• c = 1 and c = 3 average √(πp/2) ×1
• Chapman's form of the estimate is nearly unbiased ×1
• doubling the sample shrinks the typical error ×1
• each merge keeps the list size near 2^(n/4) ×1
• early repeats come at the rate a random function gives ×1
• evening the two days raises the chance that nobody matches ×1
• every product was split ×1
• every solution XORs to zero ×1
• for c = 0 every tail is a vanishing share of √p ×1
• n is a product of two primes ×1
• n is a whole number below a trillion ×1
• nobody is alone at 3,064 ×1
• nobody is alone in a room of 3,064, more likely than not ×1
• one person shares with nobody ×1
• somebody shares at 23 ×1
• T(T − 1)/2 is right on average ×1
• the chance of a match only rises as the calendar grows more uneven ×1
• the curve bends downward ×1
• the curve is symmetric about the even split ×1
• the cycle length is the order of 2 modulo the odd part of the start's order, every time ×1
• the day-probabilities add to one ×1
• the effective number is far below the true count ×1
• the effective number of days places the threshold within one person ×1
• the even year's threshold is 23 ×1
• the expected number of cancelling quadruples ×1
• the expected number of loners peaks when the room is as large as the year ×1
• the first pair agrees on the low bits ×1
• the half-way point is 23 people ×1
• the highest point is the even split ×1
• the largest share at theta one is near the Golomb–Dickman constant ×1
• the last new value leads back into the cycle ×1
• the mean length is √(πn/2) divided by the spread of the number of preimages ×1
• the modulus is a prime of at most 5000 ×1
• the option is one this view reads ×1
• the pair count is k choose 2 ×1
• the pair-count estimate settles on the effective number, not the count ×1
• the plain estimate is off by more than the whole answer soon after t = 1 ×1
• the sample holds the primes asked for ×1
• the search ends with a proper factor within forty steps ×1
• the second differences are constant, so the curve is a parabola ×1
• the second pair agrees on the low bits ×1
• the simulation agrees with the exact walk ×1
• the simulation agrees with the formula ×1
• the steps grow as roughly the square root of the smaller prime ×1
• the sweep is seasonal or weekly ×1
• the sweep starts at the even year ×1
• the symmetric-polynomial count agrees with the product on an even year ×1
• the three thresholds come in this order ×1
• the threshold follows the square-root estimate to within a couple of people ×1
• the two pointers meet within tail plus cycle steps ×1
• the uneven calendar is never less likely to produce a match ×1
• the view is one of pairs, uneven, merge, sweep, effective, rho, rholength, pollard, cost, near, circle, spacing, nearscale, strong, loners, thresholds, smallyear, rhoc, tailcycle, squaring, rtoone, early, wagnertree, wagnersuccess, wagnerwork, wagnercount, estfirst, estpairs, estcapture, estuneven, wagnersolution, wagnerlevels, estcost ×1
• the walk's survival stays within ten points of the birthday curve everywhere ×1
• they meet at a multiple of the cycle length, once both are on the cycle ×1
• two different slots ×1
• two lists grow like a half power and four like a third ×1
• what it returns divides n ×1
• with only rare kinds the plain sum is within eight per cent at t = 3 ×1

The whole library · What the figures prove