Picking Golf winners

Earlier this year, 5 of us decided to try to pick the winner of The Masters golf tourney. We decided all of us would pick 2 players including a favorite (25:1 or better) and a longshot (30:1 or higher). To make things a little more fun, we decided to put $10 bets on all 10 of our choices and share any winnings. So, we end up with $100 at risk and 10 horses. Amazingly, one of our picks was the eventual winner Danny Willet at 55:1.

We repeated this bet for the other 3 golf majors (US Open, British Open, PGA Championship). To our surprise, our group pulled off the improbable - we picked all 4 winners. We "picked" the grand slam. We had Dustin Johnson at 12:1 (US Open), Henrik Stenson at 25:1 (The Open), and Jimmy Walker at 100:1 (PGA). Sure wish we had pressed our bets a little, but that wasn't the point. We spent $400 in total bets and returned about $1960 - around $1500 profit.

Just curious how long the odds were to pick all 4 winners? I barely know stats 101, which is why I am asking the group. Could you estimate the odds by multiplying the four payouts 55x12x25x100 = 1,650,000? Or 1 time in 1.6 million tries a person will pick all 4 winners. I guess this assumes the sportsbooks got it right when setting the odds.

Appreciate any feedback, was sure fun sweating our picks.

In gerneral, when you say this AND this need to happen, it's a multiplication of their respective probabilities. When you say this OR this needs to happen, it's additive.

So when you say A AND B AND C AND D, it'll be all of their respective probabilities multiplied together.

P(Danny Willet) = 1/55 = .0182
P(Dustin Johnson) = 1/12 = .0833
P(Henrik Stenson) = 1/25 = .0400
P(Jimmy Walker) = 1/100 = .0100

Thus, P(all 4) = P(Danny Willet) * P(Dustin Johnson) * P(Henrik Stenson) * P(Jimmy Walker) = .0182 * .0833 * .0400 * .0100 = .00000061, or about 1 in 1,650,000.

However, a fun note. This is if you were to pick all of them from the beginning. Once you picked one winner the odds of getting the next one were whatever their fair odds were. This is similar to seeing 3 tails flipped in a row. What are the odds the next throw is tails? Well that's just 50/50... However if you predicted 4 tails in a row BEFORE throwing any, THEN the odds of it would be .5*.5*.5*.5 = .0625.

Quote: Romes

In gerneral, when you say this AND this need to happen, it's a multiplication of their respective probabilities. When you say this OR this needs to happen, it's additive.

So when you say A AND B AND C AND D, it'll be all of their respective probabilities multiplied together.

P(Danny Willet) = 1/55 = .0182
P(Dustin Johnson) = 1/12 = .0833
P(Henrik Stenson) = 1/25 = .0400
P(Jimmy Walker) = 1/100 = .0100

Thus, P(all 4) = P(Danny Willet) * P(Dustin Johnson) * P(Henrik Stenson) * P(Jimmy Walker) = .0182 * .0833 * .0400 * .0100 = .00000061, or about 1 in 1,650,000.

However, a fun note. This is if you were to pick all of them from the beginning. Once you picked one winner the odds of getting the next one were whatever their fair odds were. This is similar to seeing 3 tails flipped in a row. What are the odds the next throw is tails? Well that's just 50/50... However if you predicted 4 tails in a row BEFORE throwing any, THEN the odds of it would be .5*.5*.5*.5 = .0625.

That's if they made ONE selection per event... They made TEN selections per event. No way to really get an accurate likelihood, but probably around 1 in 500 given the parameters they were under (five favorites, five longshots per event)

Quote: Goodcardz

Earlier this year, 5 of us decided to try to pick the winner of The Masters golf tourney. We decided all of us would pick 2 players including a favorite (25:1 or better) and a longshot (30:1 or higher). To make things a little more fun, we decided to put $10 bets on all 10 of our choices and share any winnings. So, we end up with $100 at risk and 10 horses. Amazingly, one of our picks was the eventual winner Danny Willet at 55:1.

We repeated this bet for the other 3 golf majors (US Open, British Open, PGA Championship). To our surprise, our group pulled off the improbable - we picked all 4 winners. We "picked" the grand slam. We had Dustin Johnson at 12:1 (US Open), Henrik Stenson at 25:1 (The Open), and Jimmy Walker at 100:1 (PGA). Sure wish we had pressed our bets a little, but that wasn't the point. We spent $400 in total bets and returned about $1960 - around $1500 profit.

Just curious how long the odds were to pick all 4 winners? I barely know stats 101, which is why I am asking the group. Could you estimate the odds by multiplying the four payouts 55x12x25x100 = 1,650,000? Or 1 time in 1.6 million tries a person will pick all 4 winners. I guess this assumes the sportsbooks got it right when setting the odds.

Appreciate any feedback, was sure fun sweating our picks.

Hmmm... There were 89 players in the 2016 Master's tournament. Your group had 10 of them covered, or 11% of the field. Your odds of picking the winner at random using this method were better than one-in-ten. If you eliminated the six amateurs out of the gate, your odds could have been even better. I would guess the odds of picking all four winners by choosing 10 in each contest at 1:4,800

Thanks for all the responses.
Based on the responses, there isn't a consensus on calculating the odds of picking all 4 winners correctly.

I was shocked we hit all 4 winners, it has to be very long odds.