Michelle Loewenstein's million dollar win- feedback welcome!

Here's an obvious oversight... you define the odds for any one player to win the million fairly well... but there are three players a game who have the opportunity. If you're taking the average # of spins per game for one player as 6, then you should be doing 18 total. In fact, WOFTracker tell me that there were 22.96 spins per R1-3 in all of Season 29 (195 shows), so even that 18 is an significant underestimate, backed up by my hard-earned data (through 46 shows of S30, it's between 22-23 as well). The remaining steps still work fine.

Additionally, step C is probably a bit higher than 1/3, calling a correct letter automatically raises that... ultimately though steps C/E are very hard to calculate as sometimes the MDW is "dead upon pick-up" in a blowout game.

Regardless, simply multiplying your final result by 3 lowers ~13.8 years to about 4.6 years. Using my 22.96, we get down to about 3.6 years. I have done the rough calculations myself without any stats and some assumptions, and I have come up with once every 3-5 years.

The fact the million has not even been landed on again since that day is a testament to the actual very low odds. It just ended up occurring really early.

There's also the matter of, in a vacuum the million should be won roughly 2-3 times a decade, but that's over many many decades. We only get a few decades to live in in our lifetimes, and sometimes it's going to be just 1, sometimes 0 (the odds are probably decent for those two, but highest at 2 & 3. I dunno if you can imagine a probability curve like this, even though this is discrete?), but we aren't going to live enough (never mind the show) to see this all play out, take the average and deduce a better estimate of the true odds. Statistic deviations happen. It would be extremely rare to have 4+ though, I would imagine.

Wayo is exactly right. Even with a supposed one-in-a-million chance, you can run a million trials and end up with a number vastly different from 1. Or, if I may make a quote, "A 10% chance is pretty unlikely, but everyone knows that a one-in-a-million chance is a sure thing!"

As for responding to some of the counterpoints you made previously:

1. Wheel's production staff and/or Sony would probably be the most accurate replacements. I just wanted to make it clear that Wheel is not network-affiliated (or at least it hasn't been since the retirement of the the daytime program).

2. Of course, nothing is truly impossible, or the "My Little Genius" incident would never have happened at all. But on the flipside of that, many precautions have been taken since those days long ago and such an occurrence should be highly, highly unlikely.

3. I'm not a Wheel staffer (more's the pity), or I could say beyond doubt that they did or didn't have insurance. But given its usage on most other shows, I would imagine Wheel also employs such insurance rather than paying out $1,000,000 from their own budgets. I have no idea what the premium rates would be, but it would have to be sufficient to counterbalance both the insurance firm's operating expenses and any expectation of a win - come to think of it, knowing those rates could possibly be used to extrapolate what the actuarial staff believes the likelihood of a million-dollar win is.

4. The sample of 41 games still seems a bit low, simply because of the often-wild variance between individual shows (due to the luck factor involved at the core of the game). Individual rounds can run long or short, the game itself could be shortened due to extra fee plugs, or we could simply see a run of hard-luck programs. Ideally, I would like to include data from all episodes (which is probably what I would do if I were writing this for, say, an academic journal), but at the very least I would include something on the order of 100 episodes, randomly sampled from Seasons 26-30, to get a good idea of trends over time (as these stats could also vary between seasons).

5. The first MDBR was on 10/3/08 and $25,000 was not won (OATH OF OFFICE, where CDMA provides only two letters). If my quick check of the records is correct, there were an additional 10 MDBR's in Season 26 after Loewenstein's win, including one less than a week later (10/20/08). If you figure that the MDW has a 1/72 chance to be hit on any given spin (which is true based purely on probability, but this could be higher or lower based on spin power patterns) and that there are about 15-20 million-eligible spins in a game, you should expect at least an MDW hit (not necessarily a pickup, but a hit) about once a week.

Finally, I do agree that it's tough to determine the chances of winning a round or the whole game. If we could determine the chances of winning a round for a given puzzle, then we could also calculate the value of a lost turn at a given point and, by doing so, exactly solve the expected value for the wheel (the best we can do right now is approximate, not knowing the exact penalty for Bankrupt/Lose a Turn). In particular, the chances of winning the game can swing wildly as the show rolls on and leads grow, shrink, or change hands (particularly in the Prize Puzzle Round, where the round's winner is guaranteed at least $5,000 due to the tacked-on trip).

There are a lot a deep statistics to be had from watching and analyzing Wheel, which is why I'm glad we have folks like Wayo on hand to help us interpret the cornucopia of data. Who knows, maybe our work will help somebody win a few extra bucks on the show somewhere down the line.

This is very well thought out analysis, Mike, but did you consider hitting Bankrupt in the same round after picking up the MDW? It especially depends on how far into the round they get it, and how close they could be to knowing the puzzle. Several rounds have started with the player hitting the MDW right away, then being forced to spin because of having no money to buy vowels, then hitting Bankrupt or Lose a Turn 1-2 spins later.

MarioGS thanks, the only post million bankrupt stat I have in there is D unfortunately. What you're describing may be outside my stats ability :/ I would love to include that but I just don't know how to approximate it without analyzing every game.

WayoshiM I'm starting to understand what you're describing. I *think* the only piece I need to change here is A (and not B). It should in fact be that 23/72 number because all players are eligible to hit the wedge. however I'm still struggling to see how or why B needs to change. also is there anyway I can get my hands on the game data you mention? (the 195+ games thing).

thanks again guys,
Mike