# How did people think about probabilities before statistics was an established mathematical field? **URL:** \ **Category:** Factual Questions\ **Created:** [August 20, 2018, 9:12pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933 "2018-08-20T21:12:37Z")\ **Posts on this page:** 12\ **Page:** 2
**Author:** ![gazpacho](https://avatars.discourse-cdn.com/v4/letter/g/6f9a4e/32.png) [@gazpacho](https://boards.straightdope.com/u/gazpacho)\ **Post date:** [August 21, 2018, 2:45pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/21 "2018-08-21T14:45:04Z")
> [@Thudlow\_Boink](#): > > Your calculations are correct, but the odds are far enough from 50/50 that Chevalier de Méré was losing money consistently enough that he asked Pascal and Fermat why. One of my stat books says. > [@](#): > > De Mere told pascal that event F occurred less often than event E, but he was at a loss to explain why… From which we conclude that De Mere gambled often and kept careful records!! Event F is getting double sixes and event E is not. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [August 21, 2018, 2:56pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/22 "2018-08-21T14:56:19Z")
> [@Great\_Antibob](#): > > Sure, but not exactly even, which makes all the difference in this case. > > By the accepted ‘table’ (not really a table) of the time, the “problem of points” had a given solution. Fermat and Pascal were each independently able to show it was wrong (Pascal using his eponymous Triangle for it) and came up with the correct solution - and more or less the field of probability theory. Nitpick: There were actually two problems that Chevalier de Méré asked about. One was about the probability of rolling double sixes in 24 rolls. The other was the “[problem of points](https://probabilityandstats.wordpress.com/2016/11/06/the-problem-of-points/),” which was about the fair distribution of stakes when a game is interrupted before it’s finished. ---
**Author:** ![Ashtura](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ashtura/32/2963_2.png) [@Ashtura](https://boards.straightdope.com/u/Ashtura)\ **Post date:** [August 21, 2018, 5:45pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/23 "2018-08-21T17:45:26Z")
There is no doubt in my mind that basic probability has been understood since gambling was invented. Honestly, it doesn’t take much brains to know there’s a 50/50 chance on a coin toss, even if you didn’t express it as such. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [August 21, 2018, 6:03pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/24 "2018-08-21T18:03:07Z")
> [@bob\_2](#): > > If this wasn’t true, no one would ever buy a lottery ticket. But bear in mind that insurance also has a negative expected value to the purchaser. Utility and simple probabilistic expected value are not the same thing. ---
**Author:** ![zimaane](https://avatars.discourse-cdn.com/v4/letter/z/a3d4f5/32.png) [@zimaane](https://boards.straightdope.com/u/zimaane)\ **Post date:** [August 21, 2018, 6:43pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/25 "2018-08-21T18:43:16Z")
> [@](#): > > To set it in context, the incident which is generally credited with leading to the development of probability theory occurred in 1654. There was a gambling game being played in France where you rolled a pair of dice twenty-four times. If a pair of sixes came up on any of the rolls, you doubled your bet. If it didn’t, you lost. > > Pretty close to fair odds, I’d say-- 50.9/49.1, by my calculation. About as close to even money as you’re going to get with something that complicated. Yes, in fact, with fair dice, 24 is the largest number of rolls that still gives the house an advantage. I suppose this game developed via trial and error, but it’s interesting. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [August 21, 2018, 7:00pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/26 "2018-08-21T19:00:00Z")
Yes, with 25 rolls, the player has about 50.5% chance of winning. Seems like a rather tedious game if one play consists of 24 rolls of the dice. ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [August 21, 2018, 9:49pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/27 "2018-08-21T21:49:58Z")
I would hardly call it an unfair bet. The house has a slight edge, but that’s true of all gambling. It’s about the same as betting on red/ black at roulette with a single zero on the wheel. I agree it sounds like a tedious game. Was there more to it? ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [August 21, 2018, 10:09pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/28 "2018-08-21T22:09:05Z")
It’s already been indirectly cited, but Hacking’s _The Emergence of Probability_ really has been the crucial treatment of the subject that all the academic discussion about the issue since has either been the reactions for or against. The utterly essential interpretation. Broadly, I tend to agree with him. It was ultimately a weirdly (uniquely?) original shift in how humans could think about the world. ---
**Author:** ![zimaane](https://avatars.discourse-cdn.com/v4/letter/z/a3d4f5/32.png) [@zimaane](https://boards.straightdope.com/u/zimaane)\ **Post date:** [August 21, 2018, 10:17pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/29 "2018-08-21T22:17:21Z")
> [@](#): > > I agree it sounds like a tedious game. Was there more to it? Perhaps the rising tension as one got closer and closer to the 24th roll was enough to make it exciting. Or maybe they were just easily amused in Renaissance France ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 21, 2018, 10:30pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/30 "2018-08-21T22:30:58Z")
The ancient Chinese gambling game Pai Gow — related to Baccarat but much more complicated — was somehow analyzed over the centuries to come up with “best” play (though a _single_ best strategy was never agreed). This is quite difficult; for one thing, like Rock-Paper-Scissors, _optimal play is strongly dependent on opponent’s strategy._ When the game was introduced to Las Vegas (in the 1970’s?) different casinos had slight differences in the ‘House Way’ — the mandatory strategy when casino money was backing a hand. Caesar’s Palace, however, had a bizarre stupidity! For example, holding a Six, a Four and the two Je Joon tiles it is overwhelmingly best to set them as (9,7) — quite likely to win and extremely unlikely to lose. Caesar’s Palace House Way however was to set them as (Je Joon, 0) — almost certain to push (break even). Their rule was to _never_ split the Je Joon pair since it is impossible to lose with Je Joon. :smack: ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 21, 2018, 10:41pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/31 "2018-08-21T22:41:56Z")
> [@zimaane](#): > > Perhaps the rising tension as one got closer and closer to the 24th roll was enough to make it exciting. > > Or maybe they were just easily amused in Renaissance France There were probably side bets at increasingly mounting odds. By the time the 24th roll approached the banker betting against 6&6 might be forced to pay out hugely if shooter suddenly got lucky. He might shout “insurance”, e.g. offering to take 25-to-1 odds on 6&6 as a hedge to protect the large pile of cash collecting in front of him. As mentioned upthread, these side-bets, and requests for insurance (hedging) bets, and equitable pot splitting probably motivated some of Cardano’s own study. I’ve witnessed this scenario at least once in a high-stakes backgammon game. On the very last shake opponent wins only if he throws 6&6 — but if he does you’re busted, perhaps going deeply in debt. Wouldn’t you halt the game and shout “Anyone offering insurance?” ? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [August 21, 2018, 11:49pm UTC](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933/32 "2018-08-21T23:49:38Z")
> [@Quercus](#): > > Pretty close to fair odds, I’d say-- 50.9/49.1, by my calculation. About as close to even money as you’re going to get with something that complicated. It’s also incredibly sensitive to the accuracy of the dice. The game would be fair if double-sixes came up 1.025 times out of 36. So even a tiny push could send it in favor of the player. I’m not sure that even modern casino dice are that accurate. [Previous page](https://boards.straightdope.com/t/how-did-people-think-about-probabilities-before-statistics-was-an-established-mathematical-field/819933.md?page=1)