Two-point conversions are not required during the first two overtimes. Let p2 denote the success probability on a two-point conversion. Suppose your opponent scores 7 points in the first possession of the 2nd overtime, and you then score a touchdown of your own. If you kick the extra point, you move to the 3rd overtime. However, in that overtime you will have to start on offense, and your win probability will be 0.4773. Since kicked extra points have about a 0.985 success probability, p2 has to exceed 0.47 before you can justify going for two. In the realistic case in which p2 ≤ 0.47, the teams should never go for two prior to the 3rd overtime. (The Table entries, generated using p2= 0.4, correspond to that case.) If p2 is between 0.47 and 0.57, the team with the second possession during an overtime period should go for two if their opponents score 7 points, but the team with the first possession should kick if they score a touchdown. Consequently, as p2 rises from 0.47 to 0.57, the format becomes steadily more favorable to the team that wins the coin toss. Their win probability peaks at 0.54 when p2 = 0.57. When p2 > 0.57, even the team with the first possession should go for two following a touchdown.
