Let’s start by adding all the dice, and then do a few trials:

2 x 50 + 1 x 10 + 1 x 30 … + 1 x 100

With 5 dice, how do we get the chance to lose? We need to get 1/100 of the remaining players to win. That way it’s very rare when players have a one-in-a-million chance of losing.

Let’s add another 5 dice and let’s do 5 rolls:

2 x 50 + 4 x 10 + 3 x 30 … + 3 x 100

Now we have 1/10 chance that one of the remaining players will lose and 1/10 that all 5 players will win!

2 x 50 + 2 x 50 + 1 x 100 + 1 x 30 … + 1 x 100

Now, we have 1/3 chance that one of the remaining players will lose and 1/5 that all 5 players will win!

As you can see with that, with all these combinations the chance of winning is very high:

2 x 50 + 2 x 50 + 1 x 100 + 1 x 30 … + 1 x 100

We know this is not the right way to do it to create chance in roulette. To make sure we don’t add chance and we can really think about chance we need to reduce the numbers! We need to pick a number between 0 and 1 to make sure our chance is less than 1/100. For example, let’s add 2 dice with an odds of 2/3 of winning. How do we get the chance of winning with these odds? We would want to increase our odds of winning by a factor of 3 – so let’s do three trials each with 1/3 chance of winning.

2 x 50 + 2 x 50 + 2 x 100 + 3 x 30 … + 3 x 100

As you can see you now have 1/100 chance of winning.

2 x 50 + 4 x 50 + 3 x 50 + 2 x 50 … + 3 x 200

A better way is to pick a value between 0 and 1 to make sure we don’t get chance to lose. For example, we could say we want to pick 0.7 (0.2 x 50) or 0.35 (0.05 x 50) to make sure we don’t lose to 2 x 50. To calculate the value we need to get it we could use this formula:

0.7/

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