Warlich
Joined: Apr 27, 2012
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April 27th, 2012 at 7:15:03 AM permalink
Say that the bank rolls one die and the player one die. The player wins if her score is higher. What is the probability for the player to win (the bank wins if the scores are the same)?

What if the bank and the player may roll two times each and use the highest score?

(Say that the bank can roll his die n times and use that highest score and that the player can roll her die m times and use the higher score. Is there a general equation that can be used to find the odds for the player winning?)
DJTeddyBear
Joined: Nov 2, 2009
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April 27th, 2012 at 7:59:44 AM permalink
This sounds suspiciously like a homework assignment.

Did you work out the math for the first question? That's the easiest.

For the second (and third), I'm inclined to think that the odds are the same as the first question.

Then again, I know the math for the first question, and didn't get out my pencil for the second one yet.....
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
s2dbaker
Joined: Jun 10, 2010
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April 27th, 2012 at 8:11:43 AM permalink
We're all gonna die!!!

For the second and third, I would think it favors the house more since there is a better chance of a tie.
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Paigowdan
Joined: Apr 28, 2010
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April 27th, 2012 at 8:31:17 AM permalink
For multiple rolls, the house edge is lower, as there is less chance for a tie score the more rolls are used; the final score range is wider. 10 rolls would average 35, and tying on 35 or any number would be harder. The final score range would be 10 to 60.

Look at the chances of tyoing on a coin toss, where heads equal 1 and tails equal 0.
In one roll, your score can be only 1 or 0, and there's a 50% chance of a tie. In ten coin tosses, the possible range of scores is 0 to 10, average of 5. In a million coin tosses, the range is 0 to 1,000,000, average 500,000 and the chances of tying on 500,000 or any number would be miniscule.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
CrystalMath
Joined: May 10, 2011
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April 27th, 2012 at 8:40:33 AM permalink
Quote: Paigowdan

For multiple rolls, the house edge is lower, as there is less chance for a tie score the more rolls are used; the final score range is wider. 10 rolls would average 35, and tying on 35 or any number would be harder. The final score range would be 10 to 60.

To me, the question sounds like they will only take their highest individual roll, so the final score range would still be 1 to 6 with 10 rolls. If this is the case, it is very likely that the player and the house will tie with a 6.
I heart Crystal Math.
Paigowdan
Joined: Apr 28, 2010
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April 27th, 2012 at 8:45:57 AM permalink
Yes, if they use the single highest score and not an additive score. House edge would be huge with one roll, forget about multiple rolls.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
DJTeddyBear
Joined: Nov 2, 2009
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April 27th, 2012 at 8:46:33 AM permalink
Hmmm....

Yeah, I get it now.

The more rolls, the greater the chance for a tie.

However, with ties excluded, there always remains an equal chance of either winning.

But when ties are considered a win for the bank, the more rolls, the greater the house edge.

But that brings me back to my original question (and my feeling that this is homework).

Did you do the math for one roll each? That's the easiest to calculate.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
Ayecarumba
Joined: Nov 17, 2009
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April 27th, 2012 at 8:50:10 AM permalink
I recall that this is an actual game in a casino. I think the Wizard did an analysis.

Edit: Yes it is. See the article on "Beat the Dealer" at Turning Stone, here.
Simplicity is the ultimate sophistication - Leonardo da Vinci
Warlich
Joined: Apr 27, 2012
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April 27th, 2012 at 8:54:37 AM permalink
The first two questions are quite simple and I guess they would be on homework level. What I can't figure out (nor my collegues) is the probability when the bank gets more rolls than one (well two is rather straight forward since you can use a chart). That the bank has higher chance of winning if it has the same amount of dice is also intutive; but how do you calculate the probability if the bank has for example 3 rolls of the die and the player 4 rolls of the die?
DJTeddyBear
Joined: Nov 2, 2009
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April 27th, 2012 at 8:54:48 AM permalink
That game is based upon a two-die TOTAL.

The original poster proposed a one-die game, as well as multiple rolls taking only the highest roll.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗

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