Anyone here particularly good at math? (probability)

[Unhelpful]

38 minutes ago, zindan said:

Game 2 (blackjack): You may at any point tell the host to stop and that will be your final score.

The host rolls the dice first for you and then once you say stop you will have your score. After that he rolls for himself and tries to beat your score. If you reach 100 on your turn then the game is over and you have won.

If the dice lands at 100 you win straight away because you got blackjack

if your score goes above 100 you lose straight away.

Lets say the host rolls 66 for you and you want to keep on going then he will roll for you again, if your value goes above 100 you lose straight away and the game ends.

If you chose to stop at 66 then the host has to beat your score, same rules applies to him though. If he goes above 100 he loses and you win.


Which of these games is more likely to earn you money, which is most “probable” to win at ?

How can your score go above 100? Is this not a single 100 sided die? 

[zindan]

2 minutes ago, JoeyDM said:

How can your score go above 100? Is this not a single 100 sided die? 

Well if you tell the host to roll again. Say you roll 65 the first time and you wish to come even closer to 100 then you might ask him to roll again and what if the dice lands on 90.. In that case your score is 90+ 65 which results in a loss. 

[agent_x007]

10 minutes ago, zindan said:

Well if you tell the host to roll again. Say you roll 65 the first time and you wish to come even closer to 100 then you might ask him to roll again and what if the dice lands on 90.. In that case your score is 90+ 65 which results in a loss. 

You may have to ask the host to roll 100 times because he rolled a 1 each time...
PS. Is there a "0" on 100 sided dice ?

[zindan]

6 minutes ago, agent_x007 said:

You may have to ask the host to roll 100 times because he rolled a 1 each time...
PS. Is there a "0" on 100 sided dice ?

Yes but the chance of that happening is equal to (1/100)^100    My calculator says 0 but that's not true..  The answer is actually 0,000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 %

[Electronics Wizardy]

So i decided to make a quick simulation of this in excel. I attached the csv file if you want to play with it. Please tell me what I did wrong, this was fast.

I mainly looked at question 2.

 

I assumed 3 runs max(so if you had a total of 3 after 3 runs, I would just stop)

 

I ignored the change of your and hosts rool being the same, as its a very small change. Also ignored the change of rolling a 100 first time, but it would result in a win in this simulation anyways.

 

One big factor was what point your decided to call it. Lets look at the 5median of 3 runs with different stopping numbers(going bust is a zero)

30 61.5

40 63.5

50 66.5

60 70

70 71.5

80 0

 

So It looks like the best option for a cutoff here is about 70. Higher than I though, but due to how trying to go higher is better than settling for a very small number

 

 

Here is distribution of score with a cutoff of 70 and 3 trials

 

Here is the histogram with a cutoff of 50. Notice much fewer times going bus, but much lower scores

 

And a random diceroll(think host)(the most boring histogram)

 

Overall option 2 has much better odds it seems. It seems like you actuall have better odds than the host, so either Im doing something wrong, the host screwed up this game, or some rule is written wrong. With one dice roll odds should be about 50-50, so adding extra rolls only helps your odds it seems.

rand.csv

[wasab]

game one is the easiest. elementary schooler can figure it out. It is the number of choices for the desired outcomes over the sample space. 

 

game two is also quite simple. The main issue is that i do not know anything about playing cards. what is a blackjack? 

 

Oh, this is complicated which i am currently learning. 

[DocSwag]

6 hours ago, zindan said:

What do you mean ? 

Well it would depend on you and the dealer's strategy, no? For example, if you had a suboptimal strategy for playing the game, but the dealer had a good one, then they would win a lot. If you had a good strategy, and they had a bad one, you might win a lot.