There are 20 possible first spins. Of those 20, 7 lie above 65; 70, 75, 80, 85, 90, 95, and 100. Therefore, if you hold first at 65, there’s a 57.75% chance you’ll be beaten by one of the subsequent competitors just on her FIRST spin - holding at 65 essentially means you’re betting on yourself to lose even if your opponents weren’t allowed to spin twice.
I’m not willing to do enough number crunching to figure out the odds you’ll be beaten by a two-spin turn, but it’s got to be 70% likely or so if you hold at 65. My quick and dirty estimate is that by holding at 65 as the first player, you will be beaten by a first spin 57.75% of the time (that number is dead certain) and by a second spin about 9% of the time (that’s a rough guess based on a few quick calculations - figuring the average first spin below 65, the average expected second spin, figuring the likelihood the second spin will beat you, still not beat you or break 100, and then adjusting for the number of trials so you aren’t beaten two different ways.)
I am assuming here no player will be retarded enough to beat you on the first spin and then spin again; granting that The Price Is Right does not require a Ph.D. to compete, I’ve seen a thousand episodes and I’ve never seen anyone do that. If someone beats 65 on the second or third turn they always play conservatively and hold, so you can count on someone who follows you with a 70 to take their chances with it and screw you.
So by holding at 65, you should lose about 65-70 percent of the time.
However, if you spin on 65, you have a 65% chance of immediately losing anyway, since that’s your odds of going over 100, which means you lose no matter what your opponents do afterwards. Plus there’s a chance you can spin twice, not go over, but still lose. If you spin at 65, your average expected score the 35% of the time you don’t go over is about 82.5 - so if anyone nails 85, 90, 95, or 100, you’re history anyway. The odds of one of the two subsequent opponents getting 85 or better is a lot higher than you might think - 36% of the first spin alone, probably 45-50% overall.
So while not spinning as the first contestant at 65 will beat you around 65-70% of the time, spinning will beat you even more often, probably 80% of the time. You should hold at 65.
Clearly, of course, spinning first is a huge disadvantage. Since the second and third competitors can modify their strategy based on their spin - the third person never has to guess at all, and I’ve seen people win with 15 cents on the third spin because the first two people had to spin twice, busted, and gave the third competitor a free ticket. You can’t do much as the first competitor.