Fun FA Cup bets
January 7th, 2019 at 11:30:30 AM
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At the time of writing the draw for the FACup 4th round is a few hours away but there were some interesting bets available. However this is a maths question, which should be easy for seasoned regulars, but for others has some interesting counter intuitive points.
The other fact is that these odds are UK, so 18/1 means 18 to 1. This if you bet £1 and you win, you receive your initial wager of £1 plus £18 winnings.
There are 32 teams advancing into the 4th round (actually there are some previous round matches yet to be resolved, but for mathematical reasons assume there are only 32 teams). The draw is totally random with each team being allocated a number 1 to 32 and balls drawn out of a bag. The first team drawn plays at home and the second plays them (away). Similarly the third team drawn plays at home and the fourth plays them. This is repeated until all sixteen matches have been decided.
The bet which attracted my attention was whether four specific teams would all be drawn at home (e.g. "18/1 Arsenal, Chelsea, Man Utd and Tottenham all to be drawn at home"). My initial thought was it was 50/50 whether any given team would be at home, so the true odds could be 1/2 * 1/2 * 1/2 * 1/2 = 1/16, so a fair price is 15/1. However further thought showed this was wrong!
The puzzle is whether some of the bets are reasonable (see https://m.skybet.com/football/cup-draw-specials/event/23368077 if it's still there). Personally I thought it very clever that someone had devised such bets which are both interesting and clever.
(i) 30/1 your team to be drawn first.
(ii) 14/1 Arsenal to draw Chelsea or Tottenham.
(iii) 60/1 Arsenal to be drawn at home to Chelsea.
(iv) 18/1 four specific teams all to be drawn at home.
For the record I support Southampton so have picked the teams based on being the first named bet in the website.
The other fact is that these odds are UK, so 18/1 means 18 to 1. This if you bet £1 and you win, you receive your initial wager of £1 plus £18 winnings.
There are 32 teams advancing into the 4th round (actually there are some previous round matches yet to be resolved, but for mathematical reasons assume there are only 32 teams). The draw is totally random with each team being allocated a number 1 to 32 and balls drawn out of a bag. The first team drawn plays at home and the second plays them (away). Similarly the third team drawn plays at home and the fourth plays them. This is repeated until all sixteen matches have been decided.
The bet which attracted my attention was whether four specific teams would all be drawn at home (e.g. "18/1 Arsenal, Chelsea, Man Utd and Tottenham all to be drawn at home"). My initial thought was it was 50/50 whether any given team would be at home, so the true odds could be 1/2 * 1/2 * 1/2 * 1/2 = 1/16, so a fair price is 15/1. However further thought showed this was wrong!
The puzzle is whether some of the bets are reasonable (see https://m.skybet.com/football/cup-draw-specials/event/23368077 if it's still there). Personally I thought it very clever that someone had devised such bets which are both interesting and clever.
(i) 30/1 your team to be drawn first.
(ii) 14/1 Arsenal to draw Chelsea or Tottenham.
(iii) 60/1 Arsenal to be drawn at home to Chelsea.
(iv) 18/1 four specific teams all to be drawn at home.
For the record I support Southampton so have picked the teams based on being the first named bet in the website.
