By the third day of their honeymoon in Las Vegas, the newleyweds had lost their $1,000 gambling allowance. That night in bed, the groom noticed a glowing object on the dresser. Upon closer inspection, he realized it was a $5.00 chip they had saved as a souvenir. Strangely, the number 17 was flashing on the chip's face. Taking this as an omen, he donned his green bathrobe and rushed down to the roulette tables, where he placed the $5 chip on the square marked 17. Sure enough, the ball hit 17 and the 35-1 bet paid $175. He let his winnings ride, and once again the little ball landed on 17, paying $6,125. and so it went, until the lucky groom was about to wager $7.5 million. Unfortunately the floor manager intervened, claiming that the casino didn't have the money to pay should 17 hit again. Undaunted, the groom taxied to a better-financed casino downtown. Once again he bet it all on 17 - and once again it hit, paying more than $262 million. Ecstatic, he let his millions ride - only to lose it all when the ball fell on 18. Broke and dejected, the groom walked the several miles back to his hotel. "Where were you?", asked his bride as he entered their room. "Playing roulette". "How did you do?" "Not bad. I lost five dollars".
The rules are still not clear to me. If I bet on either R-14 or R-16, and the outcome is some other red number, I still get the 1:1 payout, right?
If you bet on Red, the payoff is 1:1 if the ball lands on any red number (including R-14 and R-16). If the ball lands on any black number or the green number, you lose your bet on Red. If you bet on R-14, the payoff is 35:1 if the ball lands on R-14, otherwise you lose that bet. If you bet on R-16, the payoff is 35:1 if the ball lands on R-16, otherwise you lose that bet. Not seeing where your confusion is.
It's impossible to know what the interviewers were looking for. The OP of the original thread never responded to any of the replies to his thread. There are several "good" answers and many bad answers so maybe any of the good answers would suffice. It's difficult to believe the interviewers would expect The Absolute Best Answer in a 20-minute time limit. Can we even determine The Absolute Best Answer? Your thoughts.
In regular roulette (the European variety with a single green number, not the extra lousy American variety with two green numbers), there are 39 possible single bets (37 numbers + Red + Black), none of which have positive expectation. In our situation above, there are 34 possible single bets, three of which have positive expectation. It strikes me that this is a great opportunity to demonstrate optimal portfolio allocation. Any takers?
Okay. And what about the rule about about R-14 and R-16? There are 3 R-14 spots. So, if I bet on one of these R-14 spots, and the ball stops at the other R-14 spot, do I get a 35:1 payoff, or not?
Not at all. When I go to a casino (never in actual facts), I expect to loose my bankroll, so my betting strategy here is to maximize the win potential, not the ending bankroll. Of course, if I wanted to maximize the ending bankroll, I would play red, and keep the bet the same ($100) to make it simple.
There are three R-14 slots on the wheel. There is only one R-14 bet square on the table. So yes you get paid if the ball lands in any of the R-14 slots.
Because of the limit of 10 spins, the outcome of any betting strategy is still mainly governed by luck. But betting red has the greatest chances of a positive P&L on 10 spins, followed far-behind by Red-16. The "optimal" betting strategy varies depending on the player's goal ... I chose to maximize the win potential, considering the initial bankroll was doomed since I was going in a casino to play that money. But if the player's goal is to preserve his bankroll while making the most of this opportunity (for example, so that he can go later play poker with the $1000), then the betting strategy would be red not red-16.
The initial bankroll wasn't doomed if you are a good poker player. That's why I changed it from the OP's original opening (there are no 'good' regular roulette players, only those who know how to stretch out their losing period). Let's assume you're a good poker player, you went to the casino expecting or at least hoping to win, and you come across this wonderful surprise of a roulette wheel putting the odds on your side for once. Now what? Still want to act like this isn't a great profit opportunity?