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This question came up while gambling.
while playing cee-low, someone tried to entice another person to bet by giving his opponent three rolls to his two, but the guy with two got to go first. He claims the odds were stacked in the other dude because of the lost roll.
The way we play:
Three rolls (normally) of three dice. Three rolls with no hits is a strike out, but the other guy still has to hit something.
456 is auto win
123 is auto lose. On either of the autos, the game is over.
To get a hit, you need to match two die and your score is whatever the third is. IE. 2-2-5, your score is a five. The next guy would have to hit that or beat it. If you get trips (1-1-1, etc) that's better than single scores, and goes the same way, 1 is lowest, 6 is highest.
So scoring priority is 4-5-6 auto win, trips (6-6-6 highest), singles (6 highest), 1-2-3 auto lose
I'm terrible at math, but I know that the second person wouldn't have close to the 75% odds that the other person said. However, I have no clue how to do this.
What are the odds per roll if you have three rolls each heads up, and what are they if the first guy has two and the second guy has three?
 
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Surely someone must be smart enough to figure this out! I must be proven right!
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Each roll of the die is a mutually exclusive event. The probability of a third roll doesn't depend on the outcome the previous two. So the odds are the same, unless I completely misunderstand the question.
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I'm just completely mindfucked by your explanation of the rules. Is this a widely known game?
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Hold on... are you saying one guy gets 2 rolls of three fair dice, and the other guy gets 3 rolls of 3 fair dice, but the guy that only has 2 rolls gets to go first? And the advantage of going first is that he has the opportunity to score a 456 first, and thus win the game?
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On November 11 2009 00:40 meeple wrote:
Hold on... are you saying one guy gets 2 rolls of three fair dice, and the other guy gets 3 rolls of 3 fair dice, but the guy that only has 2 rolls gets to go first?
Yes. Normally, who goes first is decided by a one dice roll off, with the highest number going first. In this proposition, that's traded out for the first guy having one less chance to hit numbers.
Yeah, you can still hit 4-5-6 on one shot and win.
On November 11 2009 00:39 Sadistx wrote:
I'm just completely mindfucked by your explanation of the rules. Is this a widely known game?
Yeah. Pretty much go into any ghetto and you can find people playing some variation of it on the sidewalk lol.
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Sorry, I ninja-edited that post, the only advantage of going first is that he might be able to score a 456 first and thus win the game straight up?
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On November 11 2009 00:51 Hawk wrote:Show nested quote +On November 11 2009 00:40 meeple wrote:
Hold on... are you saying one guy gets 2 rolls of three fair dice, and the other guy gets 3 rolls of 3 fair dice, but the guy that only has 2 rolls gets to go first? Yes. Normally, who goes first is decided by a one dice roll off, with the highest number going first. In this proposition, that's traded out for the first guy having one less chance to hit numbers. Yeah, you can still hit 4-5-6 on one shot and win. Show nested quote +On November 11 2009 00:39 Sadistx wrote:
I'm just completely mindfucked by your explanation of the rules. Is this a widely known game? Yeah. Pretty much go into any ghetto and you can find people playing some variation of it on the sidewalk lol.
Ah yes, the ghetto
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Yeah, that's the advantage
the second guy's chances would be dependent on what the first rolled, right? Like if he hits a 5, he's got a lot less chance to win if the other guy hit a 1.
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Is it really an advantage? Since rolling 456 is just as likely as 123?
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Yeah, they do negate each other I think, but the first guy still has the opportunity to decide the game without the other guy even touching the dice. That's gotta count for something, right??
I'm so confused 
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what happens if they tie?
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In that case, he's right in that the odds are stacked in the favour of the guy who gets an extra roll, but to get an actual percentage is a huge case-by-case solution. It basically boils down to how many cases are there that the guy who gets to go first can win straight up. There are basically only 2 cases. He gets 456 in his first roll or his second roll, and if he doesn't score any of these combinations, well it turns into a perfect normal game, except he's down one chance to beat the other guy. The probability that he gets 456 on his 1st of 2nd roll is very low, its 2/216 = less than 1%. Therefore, we can essentially consider this a problem where they roll at the same time, but one guy has 1 less roll. This doesn't give us a 100% accurate solution but its very close, since the probability of the guy winning with 456 is so low.
If we then solve the simplified probability case, you find that the odds favouring the guy with the extra roll to be about 67%, if I did everything right.
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one for one roll off, with the same rules in effect (4-5-6, etc)
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Basically, there's no advantage of going first
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i dont get the rules. what first guy only rolls 2? while 2nd roll 3? wtf
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On November 11 2009 00:54 Hawk wrote:
Yeah, that's the advantage
the second guy's chances would be dependent on what the first rolled, right? Like if he hits a 5, he's got a lot less chance to win if the other guy hit a 1.
No, the second guys roll would not be dependent on the first guys roll. The only advantage he gains by going first is that he "might" get a 456 off the bat and win the game. But like I said, the chances of that happening are less than 1%, so its not an advantage at all compared to what you're giving up.
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On November 11 2009 01:10 McCrank wrote:
i dont get the rules. what first guy only rolls 2? while 2nd roll 3? wtf
normally each person gets three rolls, someone was just angry they lost a lot of money in poker and stacked the odds to try to entice people to play him for a big pot in a dumb luck game 
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EPT
