However, I'm going to guess that you mean every time you try is going to influence the next time you try for the better (as evidenced by some paper about higher success rates for 2nd+ time entrepreneurs I remember on here), which makes sense. You learn from your mistakes, you make contacts, you have a better view of the market--so it shouldn't stay one in four every time you try.
So, no matter how many times you roll a die, you've only got one in six chance of rolling a 1 in all of the rolls?
Somehow, I think your math is slightly off.
But it seems that you mean, what's the chance that given x number of rolls, the very last one is a "1" (assuming you only need/want to get rich once). As the number of rolls increase, the chance of that scenerio (a string of non-1s with the last one being 1) becomes smaller and smaller when taken as a whole.
But, I'm glad we're all clear now.
Seriously, though, there have been a few studies of various degrees of reliability that indicate that new technology business failure rate over five years is quite a bit smaller than the old "9 in 10 startups fail" wives tale would have us believe. I wouldn't put significant weight on any particular piece of data, but it seems to be pretty consistently in that range whenever people who I would trust to know the numbers (VCs, angels, journalists covering the field, successful and famously unsuccessful entrepreneurs) talk about it.
And, among my own peers here in the valley who started during WFP07, about 1/7 of them are already rich (by some definition of rich). There were 21 groups, and I believe 3 have had exits, and I'm certain that Octopart, Weebly, Buxfer, Heysan, and Virtualmin have not come fully to fruition yet. Tsumobi might even surprise folks, as they're still slaving away in their secret underground lab in the Balkans (Josh may have actually said, "Boston", it was hard to hear at the Startup School reception due to the size of the crowd). YC certainly makes a notable improvement in the outcomes of their startups, but it's not magical, so I don't think it's a crazy idea to look at YC startups as at least somewhat representative of tech startups in general--where "tech startup" means, to me, folks who actually file the paperwork, build something, and get it into the hands of users...until you've done that, you're just another dork with a big idea (and those probably fail at a much higher rate than 9 in 10).
Anyway, we're only a year and a half into the experiment with the WFP07 group, and I expect the numbers will probably end up in the 1/3 to 1/2 range.
What I'm saying is, they're really smart guys working in a field that I know almost nothing about, and doing work that walks a razor fine line between "research" and "product". Thus, one of their biggest problems in reaching a market, reaching investors, or reaching developers, is making what they're working on into a concrete solution to a real-world problem that everyone (or at least their customers) can understand quickly. I think they'd be a bargain for anyone that hired them (either by investing in them or acquiring Tsumobi) because they are extremely smart kids with huge ideas, but I'm not sure how many people will see that based on what they're building.
And, while I'm pontificating, I don't think I'd be crazy to suggest that the best thing they could do would be to get their current code into the hands of some customers--even just a few. Because nothing guides you to providing value like having customers. And the more they pay (or the more ownership they have, if it's an Open Source project), the more value they demand...and that's a good thing when it comes to finding a need and filling it.
Put simply: Hecl is a scripting language for mobile phones, which are currently a real pain to program for.
25% chance, 4 cycles: 68.4% chance of one or more successes. 33.3% chance, 4 cycles: 80.2% chance at least one is a winner.
33.3% chance, 10 cycles (your entire career): 98.3%. Though it would be pretty hard to keep at it at 58, after 9 failures.
Of course, that assumes a reasonable level of intelligence, education, and drive.
Startups are about the best game going, as far as I can tell--I wouldn't be playing if the game was rigged against me (more than a little, anyway...sure, small companies have higher relative regulatory burden, but on the whole the technology game is actually rigged in favor of new companies, from a growth perspective).