Advantage vs. Recreational Players

[Ganchrow]

Here's an interesting question.

Let's say several players are competing in a money line contest over 100 games. The rules state that players may either bet to win 1 unit on favorites or risk 1 unit on underdogs (so a player could risk 1.1 units to win 1 unit on a bet at -110, or risk 1.0 unit to win 10 units on a bet at +1,000).

Let's say that Player A is a professional handicapper and is able to pick spreads at -110 with 60% accuracy. This is all he bets in the contest.

All the other contest particpants are recreational and only bet games at odds of +1,000/-1,500, taking the underdog every time. These players absolutely have no skill and simply pay the vig on each bet (assume there's no pricing bias in the the lines).

What are Player A's chances of winning or tying against 50 such recreational opponents? (Assume that there's no overlap between the games picked by the recreational bettors).

[slacker00]

Seems fairly simple, but I expect some kind of mathematical novelty that makes the obvious not so obvious. It's Ganchrow after all.

One question, though. How many diverse "big dog" opportunities are available within this 100 play finite window? 100? 1k? 10K? 100K? infinity?

Another question to consider is the degree of correlation between the "goofball 50" plays. It's already noted that they are taking big dogs. How much diversity of picks do the "goofball 50" implicitly exercise within that opportunity set?

In my answer, I kinda assumed infinity and low correlation until my brain snapped back to reality. We are dealing with finite numbers and probably a fair degree of correlation.

[Data]

a money line contest

spreads at -110 with 60% accuracy. This is all he bets in the contest.

[slacker00]

Yeah, I missed that.

I think Ganchrow's intention was setting up a scenario where one player in the contest takes low variance versus a pack of 50 wackos that take high variance picks.

[RickySteve]

I get 0.0520%.

[Justin7]

This is just about the worst possible contest for the pro... The variance kills his chance of winning.

[Ganchrow]

I get 0.0520%.

Sorry. People who solve problems like this in their sleep are ineligible.

[Ganchrow]

a money line contest

spreads at -110 with 60% accuracy. This is all he bets in the contest.

So by the exact wording I guess he'd be stuck betting PK -110.

But I think you know what I meant.

[Ganchrow]

One question, though. How many diverse "big dog" opportunities are available within this 100 play finite window? 100? 1k? 10K? 100K? infinity?

Another question to consider is the degree of correlation between the "goofball 50" plays. It's already noted that they are taking big dogs. How much diversity of picks do the "goofball 50" implicitly exercise within that opportunity set?

In my answer, I kinda assumed infinity and low correlation until my brain snapped back to reality. We are dealing with finite numbers and probably a fair degree of correlation.

Clearly valid points in the real world.

But when I wrote, "Assume that there's no overlap between the games picked by the recreational bettors," I had intended to imply an infinite number of candidate picks with zero correlation.

[Willie Bee]

You still haven't given enough info to a dumbass like me. What season is it, is this all just Ganchrow Theory? I expect to see this worked out on a cocktail napkin slightly stained with vodka in a couple of weeks.

[Ganchrow]

I expect to see this worked out on a cocktail napkin slightly stained with vodka in a couple of weeks.

If it stains ... it ain't vodka.

[Ganchrow]

RickySteve is of course correct. The probability of the advantage player winning is in fact under 0.1%.

Here are a few conclusions which one might readily draw from this.

• When considering the picks of even a moderate number of handicappers, drawing meaningful conclusions as to the best pickers within the group can be tricky over small 100 pick sample sizes.
• Due to the relatively higher risk inherent in betting at long odds, a successful record comprised largely of bets on moneyline underdogs is generally less statistically meaningful than a a similarly successful record comprised largely of bets on moneyline favorites.
• When competing in a money line contest against a large number of players, generally speaking the best strategy will typically involve picking a large number of (unqiue) money line underdogs. Consider that if the advantage player had simply made his picks at random (at +1,000) his probability of winning (and again we're assuming no overlap between picks) would have increased almost 38-fold (from 0.0520% to 1 out of 51).

Anyway, for all those interested, the attached spreadsheet demonstrates the solution.

You'll notice it only takes 9 recreational players for the (60%!) advantage player to have negative equity. (Thanks to RickySteve for pointing that out.)

[square1]

If I'm following all this right, changing the contest rules to fixed-profit staking (all bets are to win one unit) while leaving all players' strategies unchanged increases the Advantage bettor's chances to 79.14%. And even if the Recreational players are sensible enough to bet the favorite under the new rules, the Advantage Player still wins with 3.42% probability. So I guess contest structure matters a lot.

[Ganchrow]

If I'm following all this right, changing the contest rules to fixed-profit staking (all bets are to win one unit) while leaving all players' strategies unchanged increases the Advantage bettor's chances to 79.14%.

And even if the Recreational players are sensible enough to bet the favorite under the new rules, the Advantage Player still wins with 3.42% probability. So I guess contest structure matters a lot.

Point well taken.

Btw, I get the same as you for rec players betting at -1,500, but for whatever it's worth, I'm getting a value of 80.50% for fixed-profits staking at +1,000 (could be my mistake).

[square1]

Btw, I get the same as you for rec players betting at -1,500, but for whatever it's worth, I'm getting a value of 80.50% for fixed-profits staking at +1,000

And now that I run it again, I get 80.50% as well. I just divided column F by 10, which is dirty, but should be accurate. Not sure how I managed to screw it up the first time.

(could be my mistake).

Considering I'm the one tinkering with your sheet, not bloody likely.