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I predict that this will happen right around the 26m to 13m mark, probably happening in and around August.
I don't think it will stay there for very long, but it should for about a month.

The conditions:
PS4 will be double XB1 install base by September
Will remain as such for at least 1 month

Outcome:
One month avatar control

will take any bets, stacking month after month. First to accept gets first month, etc.

Updated with excel sales and requirements:

  PS4 XB1 GAP GAP #'s Weekly Gain Weekly cume PS4 total xb1 total ratio
10-Jan 199,544 89,206 2.24 3,216,150 21,134 21,134 18,924,344 11,070,247 58.49739
17-Jan 161,507 72,898 2.22 3,200,439 15,713 36,847 19,085,851 11,143,145 58.38432
24-Jan 148,600 73,737 2.02 3,199,313 1,128 37,975 19,234,451 11,216,882 58.31662
31-Jan 165,486 80,114 2.07 3,194,055 5,260 43,236 19,399,937 11,296,996 58.23213
7-Feb 182,217 101,702 1.79 3,215,242 -21,185 22,050 19,582,154 11,398,698 58.20962
14-Feb 207,300 106,119 1.95 3,220,180 -4,936 17,114 19,789,454 11,504,817 58.1361
21-Feb 268,384 104,375 2.57 3,160,546 59,637 76,751 20,057,838 11,609,192 57.87858
28-Feb 283,275 111,273 2.55 3,099,817 60,732 137,482 20,341,113 11,720,465 57.61959
7-Mar 240,122 92,635 2.59 3,044,965 54,855 192,337 20,581,235 11,813,100 57.39743
14-Mar 229,862 86,846 2.65 2,988,795 56,173 248,510 20,811,097 11,899,946 57.18077
21-Mar 303,472 92,764 3.27 2,870,851 117,947 366,457 21,114,569 11,992,710 56.79827
28-Mar 314,028 87,006 3.61 2,730,835 140,020 506,477 21,428,597 12,079,716 56.37194
4-Apr 249,214 84,798 2.94 2,651,217 79,621 586,097 21,677,811 12,164,514 56.11505
11-Apr 220,000 78,000 2.82 2,587,217 64,003 650,100 21,897,811 12,242,514 55.90748
18-Apr 190,000 75,000 2.53 2,547,217 40,003 690,103 22,087,811 12,317,514 55.76611
25-Apr 170,000 74,000 2.30 2,525,217 22,002 712,105 22,257,811 12,391,514 55.67265
2-May 160,000 70,000 2.29 2,505,217 20,002 732,107 22,417,811 12,461,514 55.58756
9-May 145,000 65,000 2.23 2,490,217 15,002 747,110 22,562,811 12,526,514 55.51841
16-May 139,947 65,445 2.14 2,481,160 9,059 756,169 22,702,758 12,591,959 55.46445