Probability with an Abacus: Understanding SGLs

[joncnunn]

A couple of thoughts here.

1. The primarly problem with host humans shuffling cards is that they don't suffle enough. 3 and 4 shuffles aren't enough, there will still be unnaturally high clumps of the old ordering. 7 is generally the optimum number, particlarly if cards aren't going to be distrupted one at a time. (With one at a time distruption, you can get away with 6, particlarly if you have someone else "cut" to randomize the starting point.)

2. 52 is not a particlarly good number of items for computers to puesdo-randomize using most existing algorithms. With the typical algorithms, they have best performance on numbers that can be expressed as 2 ^ N. (32 or 64.) Their wost performance is on numbers that can be expressed as ((2 ^ N) - 1) such as 63. (Both in terms of speed and randomness.)

[QUOTE] Originally posted by Hermann the Lombard

The distributions were quite different than in the "dealt" cards because the distributions were truly random. Humans don't shuffle that well.

[Solomwi]

Originally posted by Plotinus

I used to work as a croupier in a casino. One of the first things they told us was that the odds in casino games are tilted towards the house, but only very slightly (otherwise no-one would play). So how do casinos make money? Simple - when someone walks into a casino, a hole opens up in the back of their head, and all their brains trickle out of the back.

Volume, of course (aided by the hole in the head you mention ). "Stack" a game at 2% house favor, bring $10 MM across the table and boom, there's roughly $200K to the house. Obviously, the larger the sample, the more the money will tend to reflect the true game odds. Throw in the sucker bets and the same calculation applies, just with much greater than 2%.

I never worked in a casino, but do enjoy them and, thanks to understanding the math involved (yes, even with the "free" liquor flowing), think I handle being in one better than most.

[nbarclay]

Re: Probability with an Abacus: Understanding SGLs

Originally posted by Sperricles

The Myth:
So, how do we understand that 3 or 5 percent? Sadly, many of us forget and try and use a poor rule of thumb like just adding it to figure out our chances of an SGL. This logic goes something like this. "Hmm if i get 3 unique techs i'll have a 15% chance of a leader...and heck if i can get close to 20...I'll have him for sure". Unfortunately this is not quite true, but fortunately there is a way to know what your chances are!

The important thing is to distinguish between the average number of leaders you can expect and the odds of getting at least one. The math of the "myth" is accurate for calculating the average, but sometimes you get more than average and sometimes you get fewer. Thus, instead of being guaranteed exactly one leader if you are first to research twenty techs as a scientific civ, you don't get any sometimes but get two or even more other times. The situations balance out, so a player who bases his expectation of how many leaders he will get on the "myth" is actually on target - as long as he remembers that it is an average rather than a certainty and remembers that what kind of luck he's had so far has nothing to do with what he can expect in the rest of the game.

[Hermann the Lombard]

Originally posted by joncnunn
1. The primarly problem with host humans shuffling cards is that they don't suffle enough. 3 and 4 shuffles aren't enough, there will still be unnaturally high clumps of the old ordering. 7 is generally the optimum number, particlarly if cards aren't going to be distrupted one at a time. (With one at a time distruption, you can get away with 6, particlarly if you have someone else "cut" to randomize the starting point.)

Very good point! When actually shuffling at a card table (I haven't *been* at a card table lately!) I go for 7 riffles and even throw in a "Scarne Cut" somewhere along the way. I've always been a bit clumsy at riffling, so I go for the full seven.

[vmxa1]

Club dealers stir the cards in a pile, rather than hold them and riffle them in California clubs.

[Plotinus]

Originally posted by vmxa1
Club dealers stir the cards in a pile, rather than hold them and riffle them in California clubs.

In fact they do both. It varies from country to country, because how dealers shuffle is actually laid down in law. I trained in New Zealand, where we had to "wash" the cards in a huge pile and then riffle them, handful by handful, in a complex pattern, twice. It was all very vexing because if you made the slightest mistake, such as accidentally allowing the face of a card to be seen, you had to start all over again.

[vmxa1]

I think it is just club policies in southern cal. I still remember in the 60's we (players) did our own dealing. I was very glad to be relieved of that task.

My best friend dealt for a few years and played prop for one of the indian clubs.

[Hermann the Lombard]

Does the SoCal law still require lowball poker? The way I heard the story was that in attempting to ban poker gambling in CA, some genius defined the game as one in which the highest hand wins, thus failing to ban lowball. [Personally, I prefer high-low, though of course Hold 'Em is a very good game.]

[vmxa1]

Originally posted by Hermann the Lombard
Does the SoCal law still require lowball poker? The way I heard the story was that in attempting to ban poker gambling in CA, some genius defined the game as one in which the highest hand wins, thus failing to ban lowball. [Personally, I prefer high-low, though of course Hold 'Em is a very good game.]

In a word no. Most lowball games are up north. The way poker came to be was that teh state define most poker games as non skilled. The only exceptions were Draw. Low or High.

So when I started to go to the clubs in the 60's you could play Pan or Draw.

Once the Indian gaming got past the state, the doors opened and aregetting ever wider.

Sorry way off topic here.

[Plotinus]

Originally posted by vmxa1
I still remember in the 60's we (players) did our own dealing. I was very glad to be relieved of that task.

You are surely kidding me!! Players dealing? It's not possible. Imagine if David Blaine had decided to pop in for a few rounds of Blackjack. They've certainly tightened up a few things since then, that's for sure.

[vmxa1]

Nope I actually deal hands at several clubs as a player at the time. Card sharpes did exist, but were mostly known to the club and not allowed.

I could not say how much crooked dealing went on. I can tell you lots of bad dealing went on. Players that could not get the crads to the players with out fouling them.

You learned to protect your cards. If a card from someone was discarded and landed on your unprotected hand, it was fouled and could not be played (still true).