Where do the second lowest and second highest Lotto Max numbers land?
Across 1,279 Lotto Max draws the second lowest number has left 10.55 places of room behind it on average, and the second highest 10.96 places, where chance predicts 10.67 at both ends.
Chance predicts those two to carry exactly the same distribution, whatever the pool size, so the difference between them is the thing worth reading. It comes to 0.41 of a place where chance predicts none, or 1.33 standard errors. The top end has run the roomier of the two, by that much per draw. That is inside the range ordinary variation produces over a record this long.
What was measured one step in from each end
Sort a draw, set its lowest number aside and its highest, and take the next one in from each end. Draw 1279 was 01111336414351, so the number this page reads at the bottom is 11 and the one at the top is 43. The reading is the room each of them has left behind it, counting only the pool numbers the draw did not take, so 11 left nine places of room below it and 43 left eight places above. The three numbers between those two are not read here, and nor are the lowest number and the highest.
Both readings carry the same chance of being d places wide, namely (d + 1) C(N − d − 2, 7 − 2) divided by C(N, 7) from a pool of N, and they carry it for the same reason: turning the pool back to front maps every draw onto another draw just as likely as the first, and swaps the two ends while it does so. So the mirror image is not an approximation to be checked, it is what chance predicts exactly, and one column of predictions below serves both readings. Chance puts that room at twice the room it predicts below the lowest number itself, which is the figure the first and last number page reads. The column still has to be built draw by draw, because N appears in it and the draws read here come from three pool sizes, 49 up to 52. A wider pool leaves more room to be left, so the prediction grows with it, from 10.50 at a pool of 49 to 11.25 at a pool of 52. Taking today's pool and multiplying it across the whole record would invent a drift that is only the format change.
The record 1,279 draws, 16 readings
Red marks a figure outside the range ordinary variation produces
A reading of no room at all means the draw took both of the two numbers at that end of the pool, which is the one case where the second number in has nothing behind it. That needs both of them in the same draw, which chance puts at 7 times 6 divided by N times N less one, the same figure at either end.
| Room left | Chance | Below the second lowest | Above the second highest |
|---|---|---|---|
| 0 to 3 | 178.5 | 169-0.76 | 162-1.33 |
| 4 to 5 | 144.8 | 168+2.05 | 155+0.90 |
| 6 to 7 | 154.1 | 155+0.08 | 142-1.04 |
| 8 to 9 | 150.3 | 142-0.72 | 157+0.58 |
| 10 to 11 | 138.0 | 134-0.36 | 124-1.26 |
| 12 to 14 | 174.2 | 184+0.80 | 176+0.15 |
| 15 to 18 | 165.2 | 158-0.60 | 169+0.32 |
| 19 to 45 | 174.0 | 169-0.41 | 194+1.63 |
One chance column, two records read against it. A reading can run from no room at all up to 45, which is far too many values for a row each, so the stretches are cut from chance's own predictions rather than picked by hand: values are gathered up until each stretch carries a similar share of the prediction, which comes to between 138.0 and 178.5 draws a row here. That is why the stretches are not equally wide, and it is also what makes the rows comparable with one another: none of them is large merely by covering more ground. The busiest stretch is 12 to 14 below the second lowest and 19 to 45 above the second highest, while chance puts 0 to 3 first at both ends. The small figure beside each count is how far it sits from the prediction in standard errors.
The table reads 16 counts with a range, and the furthest of them from its prediction is 2.05 standard errors out. Chance alone predicts 0.7 of 16 readings that far out, so reading that many does not on its own account for a reading that far out. The table prints one of them in red. The counts in a column add up to every draw read, so they lean on one another. The predicted number of extreme readings above is still exact, because a prediction for one count does not depend on what the others do.
Read against each other instead of against the table, the bottom end has been the tighter of the two in 632 draws where chance predicts 615.4, with 40 draws level at both ends against a predicted 48.1. Chance has to split the rest of them evenly, again by the mirror image. What lies between the two readings is the inner span from the second lowest number to the second highest, and it averages 25.19 against a predicted 25.35, which is the same reading seen from the middle: the two rooms and the inner span have to add up to the pool less three, so a span above prediction is two rooms below it.
One thing has to be said about the difference in the headline. The two readings are not independent of one another: a draw that opens high tends to close high as well, and that moves the room below up while it moves the room above down. Adding the two variances together, as though the pair were independent, would leave the spread of their difference too small by a factor of 1.33, and the headline would then read 1.54 standard errors instead of 1.33. Here both figures leave the difference inside the range ordinary variation produces, so the shortcut would have cost nothing but accuracy. The figure used above comes from the pair's covariance instead, worked out exactly, so the standard errors in the headline are the honest ones.
Recent trend last 100 draws, then blocks of 20
Over that stretch the difference between the two readings comes to 1.07 of a place in favour of the bottom end, against the nothing chance predicts, which is 0.95 standard errors. That is a short enough stretch for the range ordinary variation produces to be wide, which is what the band in the charts below is for.
Mean room below the second lowest number, one point per block of 20 draws
result for the blockrange ordinary variation allowsoutside that range
Mean room above the second highest number, one point per block of 20 draws
result for the blockrange ordinary variation allowsoutside that range
Oldest block on the left, newest on the right, one chart for each end. The band is what chance predicts for those same draws, worked out from their own pools, and a point outside it is marked. No point in either chart sits outside its band. Blocks of 20 draws carry a wide band, because one draw that takes the bottom two numbers of the pool and one that opens twenty places up pull a block of that size a long way.
Applied to this draw draw 1279 · 2026-10-16
Draw 1279 was 01111336414351 from a pool of 52, and chance predicts 11.25 places of room behind the second number in at each end of a draw from that pool.
This draw sat tighter at the top than at the bottom, as 607 of the 1,279 draws read here have, where chance predicts 615.4 either way round. Where the second number in from each end sat in this draw says nothing about where it will sit in the next one, and the record above is the record of where it has sat.
Related statistics
Share this page
If this report does not answer your question, tell us what you need and we will look at building it. Contact