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June 17

Winning odds

When one says winning odds are higher, it means that in numerical expression the odds are actually lower, such as 292,201,338 to 1 in Powerball vs 302,575,350 to 1 in Mega Millions. In other words, increasing one's odds means getting lower numbers. Is this a known paradox in math? Thanks. 213.134.142.249 (talk) 11:47, 17 June 2022 (UTC)[reply]

The first rank is generally called a higher rank than the second. This is not a paradox, but a peculiarity of our use of natural language that has nothing to do with mathematics. The term odds is used loosely in the sense of "the chance that something will happen". When given as a ratio, I interpret odds of "292,201,338 to 1" as "extremely likely to happen", and "302,575,350 to 1" as even more likely, so then the chances increase with the numbers. The odds of winning the Powerball lottery jackpot, however, are very slim: 1 to 292,201,337.^[1] --Lambiam 15:00, 17 June 2022 (UTC)[reply]

Betting shop punters get round this with terms such as "short odds" (e.g. 2/1) and long odds (e.g. 20/1) - a 2/1 favourite is much more likely to win than a 20/1 outsider. Be careful with phrases such as "I got 2/1 on my horse" (bet one pound to win two) and "the horse started at 2/1 on" (bet two pounds to win one). In the case of the first horse the commentator might say "Odds of two to one are being offered about Lucky Dodger." 2A00:23C5:C719:7201:1A:5EB9:69D5:D178 (talk) 16:43, 17 June 2022 (UTC)[reply]

This may be apocryphal, but the story goes that MacDonalds once tried to introduce a Third-Pounder, for the same price as their legendary Quarter-Pounder. It failed, because way too many people complained they were getting less bang for their buck. Their reasoning was that since 3 is obviously smaller than 4, then 1/3 is smaller than 1/4. Oh dear. -- Jack of Oz ^{[pleasantries]} 23:08, 17 June 2022 (UTC)[reply]
It appears to be a true story, except that the Third Pounder was introduced by a competitor of MacDonald's.^[2][3][4] MacDonald's had earlier offered a Third Pounder, but it was sold at a higher price and used specifically Angus beef.^[5] They tried again in 2015,^[6] perhaps to test if in the meantime the American burger eater had become more fraction-savvy. --Lambiam 09:48, 18 June 2022 (UTC)[reply]

One must suppose these are people who had never seen a crime movie in which someone says, “Well, if Bill gets killed, we divide the take three ways instead of four.” —Tamfang (talk) 02:30, 20 June 2022 (UTC)[reply]