Backgammon Online

08-Jun-2010
14:08 PDT

I understand the maths, as illustrated in FAQ #27, pokhra, thanks. I just don't understand how astronomically unlikely sequences of rolls happen here as often as they do. I'm talking about things that are at odds of several million to one or more.

Given that the total number of times that the dice have been rolled on this site are around 5-6m at present, it's quite strange that any regular player on here can provide examples of games where they've been beaten by such long odds.

08-Jun-2010
16:29 PDT

If you take any sequence of 10 rolls in a row and calculate the possibility of THEM happening against all others isn't that still a zillion trillion or whatever to 1 exactly the same odds as 10 rolls of double 6?
Plus, you all have it wrong the conspiracy is against ME whenever anyone is bearing off slightly behind thats when the 66 throw is fixed up around here.

08-Jun-2010
17:22 PDT

You're absolutely right, but that's not quite what I'm talking about. I'm talking about when you've backed your opponent into a corner and, for the rest of the game, they consistently roll the perfect dice (i.e. often 1/36 or 1/18 odds against) that allow them to get out of trouble and then put you in trouble, regardless of what you do. Meanwhile, you're rolling the worst possible dice too. The odds of your opponent winning from their initially pretty much hopeless position (allowing that you play the strongest possible moves with the dice available) can sometimes be incredibly unlikely, I'm sure. Like winning the lotto unlikely, I mean. They only need to roll six consecutive 1/18 rescue rolls to trump lotto winning odds. Next time it happens to me, I'll post it here, to demonstrate the odds.

That 6 6 thing is annoying too. Especially when I'm -20 in the pip count and have just moved my final checker clear to go for the sprint finish and am thus heavily odds on to win. Typically my opponent will then immediately roll 6 6 and follow it up with a couple more high doubles for good measure, whilst I roll 1 2 three times in a row until I'm hopelessly lost. Things like that should only really happen once every several hundred games, but I don't think the dice gods favour me.

09-Jun-2010
17:52 PDT

Also, you mentioned you've seen 6 66 rolls in a row... care to provide an example link?

I seriously doubt that has happened, say, more than once among all the games ever played at this site...

If it's "just" 2 or 3 times in a row - yes, that's VERY annoying, but well, that happens...

10-Jun-2010
03:17 PDT

Sorry, I misread palwalrus' ealier post where he had six consecutive rolls of 1 2 as six double sixes. So only odds of 681k to 1 not 2 billion to 1. I can't remember the largest consecutive number of double 6s I've seen, but it's definitely several. I've far more often seen other unlikely series of rolls though, as I previously mentioned.

I possibly just don't have a deep enough understanding of the game to fully appreciate the nuances of the more fuzzy odds (e.g. the straight odds of winning from any given position, allowing for accurate play), so I've probably only seen a couple of 1 in a million games in the 800 or so that I've played, but if I see any more, I'll post them for general amusement.

10-Jun-2010
04:15 PDT

Actually, the chances are (36*36*36*36*36*36)/49.88

1 in 43,640,383 games.

Odds of winning the lotto is roughly 1 in 33,000,000

So you're 1.5 times more likely to win the lotto than to get what you did.

10-Jun-2010
04:21 PDT

Oops, I also misread. It's 1-2 rolls, not 12 (6-6) rolls, so my calculation is not right.

10-Jun-2010
04:40 PDT

The odds of winning the uk lotto are actually about 1 in 13.9m are they not?
(6/49 * 5/48 * 4/47 * 3/46 * 2/45 * 1/44 = 720/10,068,347,520 = 1 in 13,983,816)

Also the chances of rolling 6 consecutive 6 6 are simply 36*36*36*36*36*36 or 1 in 2,176,782,336. Why divide by 49.88 (the average number of rolls in a game)? That's irrelevant to the odds.

10-Jun-2010
07:09 PDT

Yes, you are quite correct.

I divided to get the odds per game...

1 in 2,176,782,336 rolls or, if you divide by 49.88, 1 in 43,640,383 games.