how to win DOND
This won't guarantee you 1M, but it will guarantee you a huge offer no matter which case you pick as yours. When the show starts, the cases are randomized but they are not truly random. The pattern that emerges is that large numbers are seldom adjacent.
Pick 26* as yours. First elimination case, pick 1. If it's large, pick 2 next. If 1 is small, skip to 3. If 3 is also small, skip to 5. Keep picking in order, so you can keep track of the pattern. Stick with odds or evens as long as they're working (see below). Also, once the banker realizes you have a strategy (this strategy in particular), he'll be soiling his shorts.
* Or 25, in which case start with 2 and follow the even/odd/big/small example above.
The semi-random element means every once in a while the even/odd rule may reverse, or that they have only swapped two cases and not truly reversed. For example, if you're working evens and you hit a big number, take the adjacent higher odd and stick with odds until the pattern reverses again, then follow the same 'they switch/you switch' pattern. Make a mental note of the points at which the pattern interrupts or reverses. You'll be going back to those once you reach 24 or 25 (whichever even/odd is working when you get there at the end of round 3).
If, in the above reversal, you skip to the adjacent higher odd and it's big, go back and pick up the next lower odd. The pattern may not have reversed, and just that one big number was thrown in as the randomizing factor. If the Next Lower Odd is also big, there was no reversal--just a one-time swap, go back to evens. If the NLO is small, switch to odds.
By the time you get to the 1-case rounds, you should have a pretty clear picture of the patterns and what the remaining cases represent, as well as the chances of 'your' case being big or small. You should also have a much better-looking right-side board than you would have had picking randomly.
Simple, innit? If you get through the auditions, practice this, a LOT. It will be much harder to keep track of with all the onstage distractions. Also, practice doing odds vs. offer. Example: You're down to 5 cases including the M. 5=20% odds, the offer should be $200K but it won't, more like 160K. Don't take that, your odds are better by 40K. At some point in almost every game, the offer equals or exceeds the odds. Never turn down an offer that equals or exceeds the odds, you can't possibly do better.
Consider the offer as gambling with your own money. Go on sense, logic, math. NOT faith, luck, stubbornness. You'll walk out with at least $250K guaranteed, probably closer to 400K. Considering some people have walked out with $10, 1/4M is winning.