Don't Pass - complete player's guide

While the Pass Line + Odds is easy to both calculate and understand, the dark side is rather counterintuitive and more complex. No surprise it's almost passee to play. To make things worse quite a few casino software providers allow odds related to the Don't Pass bet instead of the potential win and here the situation became almost hopeless. So I created this 1 page "dark side for dummies" help.

https://drive.google.com/file/d/1-gWwmfyKLf1gvoA8m_XFB8IQOmRg20tg/view?usp=sharing

It all started when I asked myself if 3x dark side bet in Playtech Craps is exactly the same as 2x in Hippodrome Casino. I felt that they are but couldn't see any quick way to solve it so... necessity is the mother of invention. Feel free to download and share. I personally think that the dark side is much less intimidating now (I mean, in Craps, not the Force). In particular, it becomes clear that while Rival has its maximums designed for Pass Line, Dragonfish has made the opposite. They started from Don't Pass and, inevitably, made the Pass Line player-unfriendly. The only combination when it make sense in online casino is 10 plus 60-45-36, with a lot of careful clicking. Doubling for 20 plus 120-90-72 doesn't make it any better. Dragonfish Craps cry for "Auto Max Odds" option.
Finally, I think it's a pure beauty that the combined edge in Sam's Town / MSS Craps is 1/1540 and players will last on average exactly 7 times longer than in stingy casinos with only double odds. It looks better than in decimal and has an obvious marketing potential.

If anyone can "see" without calculations why 3x relative to bet is essentially the same as 2x relative to win or why 20x odds lowers the combined house edge 7 times over double, I am all ears. I suspect there's more "geometric" approach to that.

PS: There is another interesting fact: the combined house edge on 6-8-10x is 3 times lower than on double odds (1/660 vs. 1/220). Hmm... looks like a new Riemann hypothesis - they're linked!

I'd be betting 6X odds max (which pays 3x-4x-5x), or 12x odds max (which pays 6x-8x-10x). When I lose two Don't odds bets on a shooter, I switch over to the Passline which may be limited to 5X odds or 10x odds, and I may limit my odds bet win to 6X or 12X.

It turns out that while odds relative to Don't Pass are in principle incorrect, it just works with 3x. This bet is much easier to play than the correct sequence 4-3-2.4x. It's also "half 3-4-5x" with 3 extra chips instead of 6, for a cost of (2/11)%. Not that bad solution after all. As a final bonus, it's like a vastly simplified 9/6 Jacks or Better played perfectly every hand.
9/6 Jacks or Better: 1-2-3-4-6-9-25-50-800 RTP = 99.54%
Playtech Craps, 3x odds on Don't Pass: RTP = 99+6/11 (0.001% higher)

After adding to the file above analysis of four odds variants that I have access to (Gamesys, Playtech, Dragonfish and 2x in real casino) I have had enlightenment. The "combined house edge" in Craps is actually the Element of Risk and it's trivially easy to calculate it from this perspective.

House edge in Craps (Pass Line) = (140/99)%
Element of Risk = 140/(99+66 * average odds)%
Element of Risk = 1.4/(99+66 * average odds) [for purists]

House edge in Craps (Don't Pass Line) = (15/11)%
Element of Risk = 15 / (11 * average odds) [in %]
Element of Risk = 0.15 / (11 * average odds) [for purists]

There is a list of games with the Element of Risk on https://wizardofodds.com/gambling/house-edge/ but Craps are not included. I think they deserve to be there and even on a honorable place. It may be one of a few games with the Element of Risk changing with impunity from casino to casino. The more odds the lower the EofR so finding the best rule is a game on its own.