I come across these types of tournament from time to time. It is usually possible to shoot for your goal in one spin, covering as many numbers as you can. As discussed in the previous thread, that ought to be the best strategy, compared to any alternative, multiple-spin approach. But I've been wondering about some possible reasons for this not to always be the case. Reason #1, I think I've disproved to myself - Roulette here is single-zero, with the rule that you get half your stake back on an even-money bet if zero comes up. So I thought there might be a benefit to starting with a sequence of one or more even-money bets, before going for the goal. However, a simple example seems to indicate it is still better to get it done in one spin - BR:$20, Target:$180 Cover 4 numbers with $5 each: chance of success = 4/37 = 10.81%. Attempt to double up first with $20 on even-money, then either cover 8 numbers (when bet wins, returning $40) or 2 numbers (when zero comes up, returning $10): (18/37 * 8/37) + (1/37 * 2/37) = 10.66%. Presumably, starting by attempting to double up twice would perform even worse. Reason #2 might be if the minimum bet increment would force you to overshoot your goal if you cover n numbers evenly, or undershoot if you cover n+1 numbers. E.g., BR $15, Target: $360, bet in increments of $0.50. This is an extreme case, as you would massively overshoot if you bet $15 on just one number. So the alternatives would seem to be either - a) Bet on two numbers, one with $10 and one with $5, and if the $5 bet wins, attempt a double-up with an even-money bet. b) Bet $7.50 on each of two numbers, and if you win ($270), cover 27 numbers with $10 each. c) Start with an attempt at a double up; if that succeeds then cover three numbers evenly with $10 bets; if the return is $7.50 do whatever is optimal to try and turn this into $360 over multiple bets (not sure what that would be). I'm not entirely sure what question I am trying to ask. Just looking for general thoughts, I suppose. Discovering which of a, b, and c is best in the above example would be instructive, but general rules of thumb, applicable to any BR and target, would be the holy grail. The closest thing to a conclusion I have at the moment is that there must be some occasions when two or more spins would have a higher probability of reaching the goal than one spin, and that an n-spin route to a given goal that incorporates some even-money bets (and hence some additional routes to the goal, involving more than n spins) presumably has a higher chance of success than an n-spin route that does not.