Here you will be playing a game based on the one in that market, or rather, your NO shares will be. 

 to generate a random number between 1 and 6 (I'm using a 1/6 chance rather than a 1/36 chance because I don't want the game to go on forever and require me to make 36 markets in expectation). If the number is 1, the game ends and the market resolves YES. Otherwise, the market resolves NO, and the game continues.

If the game continues, I will create a new market with the same resolution criteria as this one for Round 2 of the game, but I will not close that market until the total number of NO shares in it is at least equal to the total number of NO shares in this one. If that one resolves NO, I will create a third round, which will not end until the total number of NO shares is at least equal to sum of all NO shares in the previous two rounds. This continues on: Every time the market for a round resolves NO, I will create another one with the same resolution criteria, except that it will only be resolved once the total number of NO shares is equal to the sum of those for all previous rounds. The game ends once one round resolves YES.

This situation is the same as the Snake Eyes game described in the linked market, except that the people who survive or die are replaced by your NO shares, which can either cash out for Ṁ1 or become worthless, plus a few other changes that don't affect the conclusion. On the one hand, this market, and all the markets for future rounds, have a 5/6 chance of resolving NO, so it would seem that NO shares have a value of Ṁ5/6, and thus you should bet the probability down to 1/6. On the other hand, less than half of the total NO shares in this market and the future markets will actually cash out. This implies that if, after the fact, someone were to offer you the value of a randomly chosen NO share from the game, this would actually be worth <Ṁ1/2. So, if you think the probability of dying in the Snake Eyes Paradox is 1/36, you should bet this market down to 1/6, but if you think it's >1/2, perhaps you should bet this market up to 1/2.

Note: Every time I refer to NO shares here, I am referring to shares held when the market resolves. If you buy NO shares and then sell them, they don't count towards the total.