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Topic: Nontransitive Dice 


Yesterday I received in the mail from grandillusions.com what I think is going to become my favorite bar betcha: NonTransitive 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 counterintuitive 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. 


They sound cool, Think I'll look them up. fwiw 1GBP is about 2USD (1.52 anyway) 


I like their site very much. Do they still sell it ? 


Yes, they still sell this set. It's at: http://www.grandillusions.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. 


I wish these came in playing card dice. That way you could have  for example. DICE ONE Seven of Hearts Eight of Clubs Seven of Diamonds Seven of Spades Eight of Spades Eight of hearts DICE TWO Five of Diamonds Six of Clubs Five of Hearts Six of Spades King of Clubs Ace of Hearts DICE THREE Three of Heart Three of Clubs Four of Spades Jack of Diamonds Jack of Spades Queen of Hearts DICE FOUR 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. 


I like it, Nicholas. Maybe you should suggest it to Grand Illusions. 


I checked these out too and I reckon it is well worth it to keep these dice in your pocket 


[quote] On 20070612 10:37, airship wrote: I like it, Nicholas. Maybe you should suggest it to Grand Illusions. [/quote] I just placed an order and mentioned the idea. 


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... 


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. 


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 etc 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. 


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. 


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. 


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 4dice set. As you realized, neither that set is a 5050 bet, since the 62 die has a 55.56% win rate over the 40 die, while the 51 die has 50% (coinflip) with 33 die. Thus, for the 4dice game the 62 die is the best when you choose first and the 40 die is the worst. However it's a closer call then for the 3dice set. Very personal point of view, but I think the 3dice set seems more basic and more fair than the 4dice set. With the 3dice 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? 


Of course! I forgot that each dice does has a slightly different chance of winning. 


I have both sets and much prefer the 3dice 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. 


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 reallife action right too... 


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. :) 


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? 


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. 


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. 