High-Odd-Black vs High-Odd-Red in Roulette

So I read this interesting article at

http://www.roulette30.com/2013/08/an-observation-on-even-chances.html

Which basically says you have a higher probability of losing if you bet High-Odd-Black than you do if you bet High-Odd-Red.

So the idea is that if I place a bet on High Numbers, Odd Numbers and Red Colors then there is only 5 numbers that can make me lose:

2, 4, 8, 6 and 10

But if I bet on High, Odd and Black then there is theoretically only 4 numbers that can make me lose

12, 14, 16 and 18

And then the article did some math wizardry showed that with each bet being evens then the "probability" of losing all your bets would be 1/8 (1/2 * 1/2 * 1/2).   BTW, the article ignores zeroes.  So i will too.

However, he points out if we were to bet on High-Odd-Black the probability of losing all your bets is
4/36 (ignoring zeroes) which simplifies to 1/9  but..... if we bet on High-Odd-Red the probability of losing all your bets is... 5/36 or 1/7.2

So should I bet on High-Odd-Black instead of High-Odd-Red?

Errrr, no......   Because you don't win bets on how many unique numbers lose.   These are not combinator bets.    If I was offered odds of 1/8 for all my bets to lose then sure this is a winning strategy and I'd say take the house to the cleaners.   As 1/9 will yield profit on 1/8 you'd have your own edge.

That's not the bet.   The bet is 3 separate bets whose results are paid out in isolation   This is not a trixie bet, this is 3 individual bets.   And sometimes you will win more than once for a certain number.   What we really should be looking is how many times can I win across these bets.

Well, here we go....

High-Odd-Black

Oh, look, we have 54 possible wins.    Shall we see how that breaks down

• 14 numbers offer as a single win (only one bet wins (High, Odd or Black)
• 14 numbers offer as a win on two bets (High and Odd, High and Black or Odd and Black)
• 4 numbers off a win on all threes bets (High, Odd and Black)

High-Odd-Red

And we still have 54 possible wins.  And shall we see how that breaks down also

• 13 numbers offer as a single win (only one bet wins (High, Odd or Red)
• 13 numbers offer as a win on two bets (High and Odd, High and Black or Odd and Red)
• 5 numbers off a win on all threes bets (High, Odd and Red)

What does this mean?

Don't get me wrong, it's an interesting observation but it's not gonna help you win more.   the odds of winning with High-Odd-Black are still the same as High-Odd-Red (But i applaud the observation skills)

It just means, that if we bet High-Odd-Black then sure we have a greater coverage of winning numbers than High-Odd-Red but we'll win less.

It all evens out.   We're betting individual bets.  And as shown they have a different distribution.   But at the end of the day.   There are only 54 possible winning bets.....  regardless of which way you bet

And just in-case you wanna check out the math.  here is a spreadsheet with my breakdown.

https://www.dropbox.com/s/fwcgk8eb0171lus/Kavouras%20HighOddBlack.xlsx?dl=0

Hope this helps