type 1 "Double or Nothing"  any bet from 6 possible (L/H/E/O/R/B)
type 2 "Double Fun"  any combination of 2 even money bets (12 possible  LowEven, LowBlack, LowOdd, LowRed and so on)
type 3 "Triple Fun"  any combination of 3 even money bets (8 possible  LEB, LER, LOB, LOR, HEB, HER, HOB, HOR)
Of course, most popular "Double or Nothing" bet is mathematically the same in each of its six incarnations (18 chances to lose, 18 chances to double, 1 chance to win half). However, for Double Fun there are three different bets and two for Triple Fun. Long story short, the complete table look like this:
https://drive.google.com/file/d/129P7nbArPOrQsRPsXBtQ3UOQxHLEEw33/view?usp=sharing
I have a question for the community what is the variance for all these six bets and one for the Wizard  what is the highest variance possible? Bear in mind, even with £/$60 many combinations are possible, for example 45 on Red, 10 on Low and 5 on Even. The number of combinations is theoretically infinite and proof which pattern has highest (and lowest) possible variance may need a clever approach.
Return >>>  0  1/2  2/3  1  4/3  2  Total  Variance 

Even money only any of 6  18  1  0  0  0  18  37  0.980 
2 x 30 any High or Low  9  1  0  18  0  9  37  0.493 
2 x 30 ER or OB  8  1  0  20  0  8  37  0.439 
2 x 30 EB or OR  10  1  0  16  0  10  37  0.547 
3 x 20 in LER or HOB (left or right side)  4  1  14  0  14  4  37  0.307 
3 x 20 in LOR or HEB (every second)  5  1  13  0  13  5  37  0.355 
I’m not the Wizard, but here is an element of answer.Quote: MattUKThank you very much! I may have discovered casino games with record low s.d., below Pai Gow and Pai Gow Poker! :) This may mean that even money bet (any of 6) has the highest variance possible hence Double Fun and Triple Fun (and any other combination) can only decrease it. I would love if Wizard could confirm that.
What you call Double or Triple Fun is analog to playing two or three simple bets in consecutive rounds, except there is a correlation. But that correlation is very small, it is ‘almost’ independent. So looking at independent rounds gives a useful insight.
Elementary prob theory teaches that two (resp. three) independent bets at 30 have half (resp. one third) the variance than one bet at 60 .
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Please note the slight difference in ChesterDog’s table for Hi or Lo, where both bets are independent. This is due to the treatment of the Zero event: he assumes you get back half your wager, while in some casinos your bet is ‘’in prison’’, i.e. you repeat your bet. In both cases, it is not the exact same bet, so variance is a bit over half the ‘simple bet’ variance (0.9795).
If you put all your bankroll at once on a single number, but for an EV of 2.7% :
Return >>>  1  +35  Total  Variance 

All on one number  36  1  37  0.9211 
Why is it lower? Because the EV is farther from zero. In American roulette, it would be the highest variance.
Conclusion —> It is not variance or EV or House edge that one must look at, it is the RATIO OF STANDARD DEV ON EXPECTATION.
American : play all on one number. French : play all on an even bet.
Look, it may not help YOU, but that does not mean it is unhelpful.Quote: MattUKI don't know where you've got your variance from. For even money bet on European Roulette it's 4*[(18/37)  (18/37)^2] = 0.9993. The rest in equally unhelpful. The question(s) still stand  what is the highest and lowest possible variance in French Roulette (1.35% house edge, 6 basic types and almost infinite combinations between them). So far we know that French Roulette can have s.d. both higher and lower than Pai Gow Poker, which is pretty amazing.
I explained the rain to a simple girl. She kept staring at my finger instead of the clouds it was pointing to, and she said ‘’it is unhelpful’’. So I made a drawing.
The question HAS been answered. In French roulette, limited to your six types, the highest variance is ‘all on one type’ ; the lowest is ‘divide in three on HOB or LER’.
Variance is E[X^2]  E[X]^2 =
 1  (1/37)^2 = .9993 for Eur even money
 (36.25/37)  (1/74)^2 = .9795 for Fr even money
 (1225+36)/37  (1/37)^2 = 34.0804 for Eur=Fr single number bet

For the triple fun HOB, consider betting h on High/Passe, b on Black and (1hb)=o on Odd, for a total wager of 1 unit.
Return >>> 01/22h2b2o2(h+b)2(h+o)2(b+o)2TotalProba (x1/37) 41455554437
Variance = 72.25/37(72/37)h(1h)(80/37)bo  (73/74)^2
Minimizing this gives h=4/13, b=o=4.5/13 for a variance of 0.30595
Hope this helps...
On a side note, I think it would be marvelous if Wizard team could add the variance to any bet in demo mode. AFAIK no casino software provider currently offers that, even as an option. So far the house edge comparison page has unassuming note e to roulette: "Standard deviation depends on bet made". We now know that it's anything from 0.55 to 5.84.