My method of tallying stats is error-prone, so please take it with a grain of salt. It should at least be close to correct, though. It is taken from the summaries of this forum.

Surprising, the best time to deal, according to my stats is... NEVER! The contestant's case has been the highest amount eleven times. The eighth offer is second with eight times. The fourth offer and ninth offer are tied for third with seven. Surprisingly, dealing at the second offer (three times) has been correct more often than dealing at the third offer (twice). Here is the complete rundown:

BEST AMOUNTS IN GAMES:

Contestant's Case - Eleven Times. (All resulting in OBWs.)
Eighth Offer - Eight Times.
Fourth Offer - Seven Times.
Ninth Offer - Seven Times. (Resulting in many of the TBWs.)
Fifth Offer - Six Times.
Sixth Offer - Four Times.
Seventh Offer (The one most taken by contestants) - Three times.
Second Offer - Three times.
Third Offer - Twice. (Less often than the second offer!) (Once until Today!)
First Offer - Never.

It is very dubious that, of all the late-stage amounts, the seventh offer is the most taken by the contestants, and have been the best amount the least amount of times.

Here are the amounts most often dealt by the contestants:

Seventh Offer - Fourteen times.
Sixth Offer - Eleven times.
Eighth Offer - Eight times.
Contestant's Case - Seven times (And, never when it's been correct!).
Fifth Offer - Six times.
Ninth Offer - Twice. (Only!)
Fourth Offer - Once. (Only!)
First Offer - Never. (As you would expect!)
Second Offer - Never. (As you would expect.)
Third Offer - Never.

Of Note: In late-game stages (From One-case-at-a-time stages until the end), it should be noted that the seventh offer is the most taken and the sixth offer second most taken, and among the late-game stages, the seventh offer is the worst (In fact, of all the stages, including the early stages, only the first offer and third offer is worse than the seventh offer), and the sixth offer, the second most taken, is the next worst place to deal. Therefore, the sixth and seventh offers have been preventing a lot of OPWs this season.

Also surprising: That the fifth offer is taken six times (while there is only a 17% chance of taking out the highest amount and no chance of taking out the two highest amounts) while the fourth offer has only been taken once and has a 25% chance of taking out the highest amounts, and if I calculated correctly, about a 4% chance of taking out the TWO highest amounts. Yet, the fifth offer has been correct to deal only one less time than the fourth offer, and dealt at way more often!

Also interesting: Contestants have taken the eighth offer eight times (And, of course, the sixth and seventh offers more than anytime.), and the case amount seven times, but have only taken the ninth offer TWICE!

Based on these stats and observations, I would then conclude that if you want to play a wimp game, deal at the fourth offer. If you want to play a gambling game, go on until at least the eighth offer, no matter how risky the board is. But, you way want to consider dealing at the fifth offer and cut your losses if its a one-case game at that point.

Wow, that's very fascinating. Thanks for posting that!

-Joe R.

Thanks JR.

I also tallyed the results.

OBWs: Nineteen!
TPWs: Twelve.
TBWs: Eight.
OPWs: Six.

The nineteen OBWs were resulted from eleven players that should have went all the way for the case, the seven players that do go for the case, and that yet no player has gone for the case when correct to do so. That is eighteen OBWs right there. The nineteenth one, IIRC, came from dealing with two high amounts in play, having BOTH high amounts in the Final Two, and the second-highest amount in case.

It's nice that TPWs are happening more often than TBWs. Many of the TPWs came from dealing at the seventh offer when dealing at the eighth offer was correct. Other TPWs resulted from nice comeback games. The TBWs did mostly come from wimpiness, untimely dealing, greed, or a combination of the above, not harsh penalty offers or inflated proveout offers. While there were several inflated proveout offers, more low amounts went before the big one, and wimpiness caused the TBWs a lot more than inflated proveout offers.

Only six OPWs have been scored out of 45 games. That is only 13%. Assuming ramdon dealing with no reguard to plans, listening to your helps, reguard to the amounts still in play and how they go, and strategy, you'd still expect to score an OPW 10% of the time, and they're only doing slightly better using actual planning, board studying, and strategy! Although I shouldn't expect OPWs to even be a semi-regular occurance, I'd still expect them to happen in at least 20% of the games.

The banker has won 27 games while the players have won 18. So, players have won 40% of the games. What is really disturbing is the OBW-OPW ratio. While I definitely expect OBWs to happen more often than OPWs, so far this season, OBWs have been outnumbering OPWs by a three-one ratio! That is disturbing. Why is that?

Conclusion: It just seems like, this season, we keep getting the gamblers when we need the wimps and the wimps when we need the gamblers. Although DOND is pretty much strictly a game of luck, it does seem like OPWs are happening way less often than they should and OBWs are happening way more often than they should. At least TPWs are happening often enough and TBWs haven't happened that often.