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Topic: Nontransitive Dice
Message: Posted by: airship (May 15, 2006 07:15PM)
Yesterday I received in the mail from grand-illusions.com what I think is going to become my favorite bar betcha: Non-Transitive dice. I ordered both sets, the one with four numbered white dice, and the other with three colored dice with pips, and I think the colored ones with pips will play better in the bar.

The bet is simple - tell your mark 'take any one of these 3 dice, I'll take another, and whoever loses over 10 rolls buys the next round.' Of course, the dice are rigged with varying numbers of pips. But the killer is that, even if they notice, you just say 'sure, I thought you realized that, but you always have first choice, so you've got the advantage.' But they don't, because blue beats green; green beats red; but red beats blue. So no matter what your mark picks, you can pick another die that beats him 6 rolls out of 10.

It is totally counter-intuitive that one of the two remaining dice can [b]always[/b] beat the initially chosen die, no matter which color your mark picks.

These were 3 pounds British, whatever that works out to in real money, plus shipping from the UK. I ought to make that up my first night out.
Message: Posted by: acmp (May 26, 2006 08:04AM)
They sound cool, Think I'll look them up.

fwiw 1GBP is about 2USD (1.5-2 anyway)
Message: Posted by: Mehtas (Jul 14, 2006 06:46PM)
I like their site very much.

Do they still sell it ?
Message: Posted by: airship (Jul 17, 2006 11:53AM)
Yes, they still sell this set. It's at: http://www.grand-illusions.com/toyshop/ntdice2/
3 pounds British plus shipping. I bought some 'Sicherman Dice' and the other set of nontransitive dice while I was at it. Fun stuff.
Message: Posted by: NJJ (Jun 12, 2007 03:15AM)
I wish these came in playing card dice.

That way you could have - for example.

Seven of Hearts
Eight of Clubs
Seven of Diamonds
Seven of Spades
Eight of Spades
Eight of hearts

Five of Diamonds
Six of Clubs
Five of Hearts
Six of Spades
King of Clubs
Ace of Hearts

Three of Heart
Three of Clubs
Four of Spades
Jack of Diamonds
Jack of Spades
Queen of Hearts

Two of Clubs
Two of Hearts
Nine of Diamonds
Nine of Spades
Ten of Hearts
Ten of Diamonds

The dice would look more 'legit' and the pattern would be harder to spot.
Message: Posted by: airship (Jun 12, 2007 09:37AM)
I like it, Nicholas. Maybe you should suggest it to Grand Illusions.
Message: Posted by: chappers (Jun 12, 2007 11:24AM)
I checked these out too and I reckon it is well worth it to keep these dice in your pocket
Message: Posted by: NJJ (Jun 12, 2007 04:47PM)
On 2007-06-12 10:37, airship wrote:
I like it, Nicholas. Maybe you should suggest it to Grand Illusions.
I just placed an order and mentioned the idea.
Message: Posted by: fless (Jun 19, 2007 06:12AM)
Hmm, stupid newbie question maybe, but how about this one? For each 3 bets I netto 1 bet right? Problem is I know quite a few highly analytical people and I will probably raise suspicions by letting them chose first every time. If we alternatve on chosing first, I still netto 1 bet for each 6 bets, right? Just a thought...
Message: Posted by: NJJ (Jun 19, 2007 06:53AM)
Not sure what netto means..but

If they choose first you have a win 2/3 of the time
If you choose first you have a win 1/2 of the time.

Therefore, over a large number of games, it will be as if you never played the games where you pick first.
Message: Posted by: fless (Jun 19, 2007 07:22AM)
Sorry about confusion; this what I suggested:
1st game: opponent choose first
2nd game: I choose first
3rd game: opponent choose first
4th game: I choose first

When playing 12 games this way, I will on average show a 2 bet profit, right? The 6 games when I choose first equal out, I win 3 and opponent wins 3. The 6 games when opponent chooses first I win 4 and opponent win 2. This way I will, hopefully, not raise any suspicions.
Message: Posted by: Dave V (Jun 19, 2007 12:13PM)
It'll take longer to get ahead, but the math sounds good. Maybe you can pull ahead early by being the second chooser for a while and only offer to switch if challenged.
Message: Posted by: airship (Jun 19, 2007 02:34PM)
Actually, the math is more complicated than 50/50 when you choose first.

Given that the mark has no clue which die beats which other die, If you choose first, choose the red die. It has a 55.56% ((69.44%+41.67%)/2) chance of winning when you average its odds against the two remaining choices. If you pick blue first, your chance is only 43.06% ((30.56%+55.56%)/2). The green die is the only one that averages to exactly 50% ((41.74%+58.33%)/2).

So pick red most of the time, green occasionally to mix it up, and avoid blue like the plague, and you should come out steadily ahead.
Message: Posted by: fless (Jun 20, 2007 03:57AM)
Dave, right. Though, I think the slower win rate will add to the plot, since the edge will not be too obvious. And it is still very good, imagin a profit of 2 bets for every 12 hands of poker? At least I don't show that kind of profit... ;)

Perfectly correct there airship. I actually discussed the 4-dice set. As you realized, neither that set is a 50-50 bet, since the 6-2 die has a 55.56% win rate over the 4-0 die, while the 5-1 die has 50% (coinflip) with 3-3 die. Thus, for the 4-dice game the 6-2 die is the best when you choose first and the 4-0 die is the worst. However it's a closer call then for the 3-dice set.

Very personal point of view, but I think the 3-dice set seems more basic and more fair than the 4-dice set. With the 3-dice you can also control the win rate. I will definitely give them a try with my analytical spouse and some friends and see whether they fall for it. What is your experience?
Message: Posted by: NJJ (Jun 20, 2007 07:02AM)
Of course!

I forgot that each dice does has a slightly different chance of winning.
Message: Posted by: airship (Jun 20, 2007 09:52AM)
I have both sets and much prefer the 3-dice set for three reasons:

(1) It has pips, not numbers, so it seems more natural. With some marks, you can even get by with not pointing out that they're pipped abnormally!

(2) The three colors make the dice easier to keep track of than having four dice all the same color. Again, this helps keep the heat off the pips.

(3) 3 dice vs. 4 dice seems less tricky and confusing to the mark.
Message: Posted by: fless (Jun 21, 2007 05:08AM)
Hmmm... another one: how do you talk people into the wager by the way? I mean; Hey, let's throw some dice! and then you materialize the dice out of nowhere, or how do you do it? Will people take the wager, or do you offer them some edge? "let's roll 10, and I bet I win at least 6 of them" (then the mark has to choose first to give me a reasonable edge). Or is the edge to allow mark to choose first?
I love this idea, I want to get the real-life action right too...
Message: Posted by: airship (Jun 21, 2007 04:28PM)
I usually present it pretty casually:

"Hey, lets toss a coin to see who pays for the next round. Oh, wait, I think I've got some dice in my pocket. [Pull them out.] Let's roll for it instead. Best out of 10 wins, loser pays. Here. You can pick your lucky color first."

Of course, I only do this stuff for friends, and they know they're going to get beaten, but they usually bite just to see what I've got up my sleeve. :)
Message: Posted by: Dave V (Jul 7, 2007 12:59PM)
I'm waiting on mine to arrive now.

Ten rolls sounds like they need a lot of patience. What's a good minimum number before you see enough of a trend to be ahead without boring them?
Message: Posted by: airship (Jul 9, 2007 02:26PM)
Dave, I'm talking about sitting around with friends in a bar setting, where you can have a couple of people rooting for each of you while you waste some time and consume a beer.

Your advantage is about 55%-69%, depending on the dice chosen. A 55% advantage isn't much, so the more throws, the better. Even ten rolls is pushing it. But the idea is that, over time, you win more games than you lose. And if your mark wins a few, that makes it seem more fair.
Message: Posted by: Dave V (Jul 10, 2007 09:50AM)
I just got mine last night. Maybe I'm just lucky but I won 4 out of the first 5 rolls. Changed dice and still won 4 out of 5. One more change and I rolled 3 out of 5. Maybe I'll just go with it and if I hit a streak like that again I'll just quit while I'm ahead.