I play roulette and want to answer this probability question. There are 38 numbers on a double zero roulette table. Suppose that I have 10 chips. Is it better to play all 10 chips on one chip per number for one spin, or is it better to bet one chip on one number for 10 consecutive spins? More importantly what formula do I use to solve this?
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Need help on what formulas to use
- Thread starter Tollens
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Which system will win the most money over the long run on a roulette table?
1. Betting 10 straight up numbers on one spin.
2. Betting 1 straight up number for 10 spins.
A double zero roulette wheel has 38 numbers. The above system is meant to be played on straight up numbers which pay 35:1. So if I bet on 10 numbers, then only one unit will win and nine units will lose.
It might be easier to think about rolling a 38 sided die. In 1) you get to pick 10 numbers for one roll and in 2) you get to pick 1 number for 10 rolls. It costs you one unit to pick a number, but if it rolls on your number, then you get the unit back plus 35 more units.
So what I want is the formula to figure out which way would produce the biggest profit in the long run given the same amount of units for each system. In 1) you have a better chance to win, but in 2) you can win more often.
Which system will win the most money over the long run on a roulette table?
1. Betting 10 straight up numbers on one spin.
2. Betting 1 straight up number for 10 spins.
A double zero roulette wheel has 38 numbers. The above system is meant to be played on straight up numbers which pay 35:1. So if I bet on 10 numbers, then only one unit will win and nine units will lose.
It might be easier to think about rolling a 38 sided die. In 1) you get to pick 10 numbers for one roll and in 2) you get to pick 1 number for 10 rolls. It costs you one unit to pick a number, but if it rolls on your number, then you get the unit back plus 35 more units.
So what I want is the formula to figure out which way would produce the biggest profit in the long run given the same amount of units for each system. In 1) you have a better chance to win, but in 2) you can win more often.
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For the bet all strategy
Pr[win] = 10/38
WinGain = 36 (right? you get the unit you put on the winning number back plus 35)
E[gain] = Pr[win]*WinGain = (10/38)*36 = 9.47
For the bet 10 times strategy
Pr[win] = 1/38
WinGain = 36
10 independent spins
For each spin E[gain] = 36/38
The total E[gain] is this summed 10 times or (10/38)36 = 9.47, the same answer as with the bet all strategy.
Given the assumption of 10 independent spins there is no difference in the strategies.
It does not make sense to me that both give the same probability for profit. Option 1) pays out a max of 35, but option 2) can pay out max 350
So option 1 and option 2 have the same chance to win?
Romsek,
Thank you very much for the calculations. This is interesting, it's like a logical illusion. I wonder what most people would pick if they were given a choice of one chance to hit at 10/38 or 10 chances at 1/38 and you get one million bucks on a win.
Thanks a ton
Thank you very much for the calculations. This is interesting, it's like a logical illusion. I wonder what most people would pick if they were given a choice of one chance to hit at 10/38 or 10 chances at 1/38 and you get one million bucks on a win.
Thanks a ton