Roulette Wheel Game

If there was a roulette wheel that has 100 numbers on it, and this includes the green 0 and 00.

The rules are simple, every day you get 1 spin:

1) If you land on 0 or 00, you lose your whole account. (2% chance)
2) If you land on the other 98 numbers besides 0 or 00, you make +3% of your account every spin. (98% chance)

So if you spin it 5 times, let's not take compounding into effect, you will make +15% overall.

Would you play this game? Why or why not? What would your long term strategy be, if any?

What odds would you be willing to play (if these odds are too risky for you)?

It's always interesting to see what everyone's risk tolerance is.

 

I'd put 50% of my original account on every spin and rathole the rest. I have a lot of time.
So if I started with 20 bucks I would put $10 on every spin until I had to take a break (or went broke.) And then I would go home and think about it. And If I liked it I would show up next day with $40 and a $20 bet. Once I got to a thousand dollars that would be real money and I would have to ask myself if I am ok with losing 2k on two spins. And let's face it, If I am reduced to going to the casino to play roulette everyday I probably don't have a lot going on, and 2k could be a lot for someone like me in my situation.

 

Not sure if you made a mistake or if this is a trick question.

If you meant to say 'you lose your whole account' then don't play the game. Risk of ruin is certain.

But if you meant instead 'you lose the whole amount you bet', which is allowed to be less than your whole account, then you should bet the following fraction of your account :

.98/|-1| - .02/.03 = 31.333333%

Your account will grow 0.165% on average per spin.

 

Let's say, you are allowed to remove any winnings, but you may not bet less than the original account amount.

 

2% chance of losing the entire account is too high. Plug that into the expectancy formula and see for yourself. Don't average down.

 

You'd have to win 34 times in a row just to barely equal your account. That works out to almost a 50/50 bet that you'd win your account size before losing your original account. That's not a smart bet, that's a bet for degenerate gamblers.

 

10 simulations with 10 million draws each:
draws=10000000 winScore=29399223 lossScore=20025900 --> w/l=1.468 pWin=59.48%
draws=10000000 winScore=29398818 lossScore=20039400 --> w/l=1.467 pWin=59.47%
draws=10000000 winScore=29399451 lossScore=20018300 --> w/l=1.469 pWin=59.49%
draws=10000000 winScore=29401134 lossScore=19962200 --> w/l=1.473 pWin=59.56%
draws=10000000 winScore=29399478 lossScore=20017400 --> w/l=1.469 pWin=59.49%
draws=10000000 winScore=29399388 lossScore=20020400 --> w/l=1.468 pWin=59.49%
draws=10000000 winScore=29400237 lossScore=19992100 --> w/l=1.471 pWin=59.52%
draws=10000000 winScore=29400420 lossScore=19986000 --> w/l=1.471 pWin=59.53%
draws=10000000 winScore=29400420 lossScore=19986000 --> w/l=1.471 pWin=59.53%
draws=10000000 winScore=29401611 lossScore=19946300 --> w/l=1.474 pWin=59.58%

And here's the C++ code:

Code:

/*
sim1.cpp

Compile:
  g++ -Wall -O2 sim1.cpp
*/

#include <cstdio>
#include <cstdlib>
#include <ctime>

using namespace std;

int main()
  {
    srand(time(0));

    const size_t N = 10000000;
  
    const size_t M = 100;      // 100 possibilities in each draw
    size_t win = 0, loss = 0;
    for (size_t i = 1; i <= N; ++i)
      {
        const int r = rand() % M;
        if (r == 0 || r == 1)
          loss += 100;
        else
          win  += 3;
      }
  
    printf("draws=%zu winScore=%zu lossScore=%zu  --> w/l=%.3f  pWin=%.2f%%\n",
      N, win, loss, double(win) / double(loss), double(win) / double(win + loss) * 100.0);
  
    return 0;
  }

 

OK I blew it. You get on average 50 spins before losing your account. So your net gain (on average) is

49*.03 - 1 = .47= 47%

 

STAW AWAY from the dreaded wheel man ! And that's good advice !
The US has, as pointed out, even less chances with 0 and 00. Europe usually only has one 0 and it's still a suckers gamble.

 

The calculation will differ depending on what you do with the removed winnings. If you bought real estates with it, and subsequently your account get wiped out, would you eventually sell the real estate and put the money back into your strategy? If that is the case, then the removed winning just act like a reserve. It would not make the strategy profitable. How money is managed will not turn a losing strategy into a winning strategy.