Consider the following bets:
1. Bet an even chance with 1 unit for 2 spins? (for example Black, Black)
or
2. Bet 2 dozens for 1 spin? (for example 1rst dozen, 2nd dozen)
Are they equal? Which one is better?
Which one would you choose if your life depended on winning one unit?
As an answer to "which bet is better?", I'm no math guru, but I'd say just look at the EV (expected value/expectancy) for each of the bets and compare.
First excluding the house edge for the sake of simplicity:
Bet 1:
50% chance of breaking even
25% chance of losing 2 units
25% chance of winning 2 units
EV = 0%
Bet 2:
33.3% of losing 2 units
66.6% chance of winning 1 unit
EV = 0%
Therefore both bets are equal.
Now adding the house edge to the picture, both bets would still be equal IF Bet 1 was played for only 1 spin. But since Bet 1 is played for 2 spins, that means a longer exposure to the zero. So Bet 2 is "better".
Now if my life depended on winning one unit, I would pick Bet 2 with no hesitation, not exactly because of the above, but simply because with Bet 1, once you lose the first spin, there is no point in playing the second spin because I would only keep my life if I won 1 unit, not break even. The same with if I win the first spin, there is also no need to continue playing because my arse is already saved. So to simplify:
Bet 1:
47.3% chance of saving my arse
52.7% chance of losing my life
Bet 2:
63.9% chance of saving my arse
36% chance of losing my life
:)
Good analysis. Totally agree.
This shows that although in roulette all bets have the same EV (it is an exceptionally good balanced game), the ARE better and ors suited bets according to your specific intention. If for example our intention is to get the most secure profits we'll choose bet 2, if we prefer max profits we choose bet 1.
My humble opinion is that apply math and probability based upon 37 or 38 degree of freedom is a waste of time as fluctuation come and go in various ways wish we can not predict or can we ...
O_o