ORIGINAL: Mziln
Which if no other chits are generated brings us into 1942 when you start drawing 2 USA entry chits per turn which would add 7 entry points (rounded) per turn to a entry pool.
In every game I have seen, there are more than the minimum number of chits. A typical game for us, runs something like this:
3 chits at startup
2 pulls at end of turn
+1.2 (avg) Axis dow poland
-0.9 Allies dow Germany
0.3 Axis Dow Yugoslavia
0.3 Axis Align Rumenia
0.3 Axis dow Denmark
-0.7 USSR Controls East Poland
0.4 Japan takes on Chinese city
Total 1939: 5.9 chits (avg)
1940:
6 at end of turn
- 0.4 USSR occupy baltics
- 0.8 USSR DOW Persia
0.8 Japan takes 2 chinese cities
0.7 Italy DOW UK or France
0.3 Germany DOW Holland
0.8 Germany DOW Belgium
0.3 Germany Align Hungary
0.3 Germany DOW Greece
1.8 Vichy
Total 9.8
1941
6 at end of turn
0.8 Germany + Italy dow USSR
0.7 Japan dow USSR
0.3 Germany align Finland
0.3 Germany Align Bulgaria
Total 8.1
Total: 23.8
Or just enough for option 34 with a little luck in nov/dec 41.
A more detailed average, assuming mwif (with my averages above):
1939: 5.9 * 2.26 = 13.3
1940: 9.8 * 1.87 = 18.3
1941: 8.1 * 2.22 = 18.0
Total : 49,6 Total chit points
Now, the total needed (MINIMUM) for option 34, is a total of 17/17 entry and 9/8 tension, or 51 total.
Getting totally average chits, option 34 could be taken an jan/feb 42 with these rules, provided they are perfectly distributed between the pools. Mar/apr would be just as likely, since pools are rarely that perfectly balanced. (The is slightly late compared to the boardgame, since mwif will have comparatively more 1940-chits drawn.)
The problem is that EVERY SINGLE DRAW has a standard deviation of about half a turn. If the draws are independant from each other, that means that the standard devation from 25 draws is about 0.5 * SQRT(25) = 2.5 turns (bi-directional). On top of this comes the random factor of the actual chit roll for 21 of those chits, which is about 2 more chits of uncertainty, for about 1 turn of added standard deviation. sqrt(2.5^2 + 2^2) = 3.2, or about 3 turns.
It should be possible to prove this (gu)estimated standard deviation with a simulation.
Note that some entry actions were left out, mainly:
- No french or UK dow on Italy. Italy is able to fight just one enemy until option 34.
- No Japanese aligning of minors prior to option 34.
- Only a limited japanese offinsive in china (Taking out either the communist chinese, or the southern resources, but not both.)
Now, with a conservative estimate of the value of 1 turn for option 34 of 50bp, this means a typical pure luck factor from US entry alone of about +/- 150bp, trying to be conservative.