The reverse lottery -- what is the highest one you'd accept

[Dan Druff]

Say you had the opportunity to pick a number between 1 and 1,000. If your number matches a pre-selected number in that range, you have to pay $1,000. However, if your number does not match (which will happen 99.9% of the time), you will get $2. Obviously this is highly +EV. Would you do it? I assume everyone on this forum would say YES.

However, let's change this to a number between 1 and 1,000,000, where if your number matches, you owe $1,000,000. If it doesn't, you get $2. Would you do it (provided you had at least $1,000,000 in assets)? I wouldn't. I bet a lot of you also wouldn't.

So it's a matter of risk/reward, obviously.

What is the highest odds number where you'd accept it? 1 in 500,000? 1 in 100,000? 1 in 20,000?

Assume that you can only do it a maximum of 50 times, and you can't pool your resources together with others.

[sonatine]

i wouldnt do any of this shit because i work for a living and have no time for foolishness.

[RegGaymer]

First example you have a $1000 liability to make $50 profit

Second example a mill for the same profit, of course no one would bother if the parameter remains the same (50 spins) because what’s 50 bucks when you’re liquid af

Change it accordingly so that it’s 5000 tries and any insurance firm will happily take the free 5 gees

[lol wow]

Puhhlease engaging in foolishness literally sonatines middle name

[incognito81]

I'd engage auto spin

[gut]

i pick #767,330, paypal me my $2 plz

[thesparten]

Absolutely not!!!

I would only play that game at 1k..

Anything other then that wouldn't be worth it.

Let's say I get $20 but could lose 10k..

That also changes it even at same odds.

Loseing 1k sucks but loseing 10k hurts.

[duped_samaritan]

If a $1 miss pays out $2 + original $1 back ($3), then you just put 1 millionth of your net worth on every number and double your net worth 100% of the time.

If it just pays out $2, then it's actually -ev since you would end up losing $2

[Dan Druff]

If a $1 miss pays out $2 + original $1 back ($3), then you just put 1 millionth of your net worth on every number and double your net worth 100% of the time.

If it just pays out $2, then it's actually -ev since you would end up losing $2

You aren't paying $1 for each entry. You're paying nothing. You guess a number. If it matches, you pay the large amount. If it doesn't, you get $2.

Looking at the 1 to 1,000,000 example:

Let's say you took a million entries at once, and chose each number, guaranteeing you would win 999,999 times and lose once.

999,999 x $2 = Win $1,999,998
1 x $1,000,000 = Lose $1,000,000

Total = Win $999,998

[duped_samaritan]

If a $1 miss pays out $2 + original $1 back ($3), then you just put 1 millionth of your net worth on every number and double your net worth 100% of the time.

If it just pays out $2, then it's actually -ev since you would end up losing $2

You aren't paying $1 for each entry. You're paying nothing. You guess a number. If it matches, you pay the large amount. If it doesn't, you get $2.

Looking at the 1 to 1,000,000 example:

Let's say you took a million entries at once, and chose each number, guaranteeing you would win 999,999 times and lose once.

999,999 x $2 = Win $1,999,998
1 x $1,000,000 = Lose $1,000,000

Total = Win $999,998

Ahhh...If you can only guess one number, I think you'd need to have a net worth of hundreds of millions to justify exposing yourself to that kind of risk for such a small reward.

[RS_]

Say you had the opportunity to pick a number between 1 and 1,000. If your number matches a pre-selected number in that range, you have to pay $1,000. However, if your number does not match (which will happen 99.9% of the time), you will get $2. Obviously this is highly +EV. Would you do it? I assume everyone on this forum would say YES.

However, let's change this to a number between 1 and 1,000,000, where if your number matches, you owe $1,000,000. If it doesn't, you get $2. Would you do it (provided you had at least $1,000,000 in assets)? I wouldn't. I bet a lot of you also wouldn't.

So it's a matter of risk/reward, obviously.

What is the highest odds number where you'd accept it? 1 in 500,000? 1 in 100,000? 1 in 20,000?

Assume that you can only do it a maximum of 50 times, and you can't pool your resources together with others.

The advantage in terms in dollars is roughly the same for all the scenarios. At 100, it's 98c. At 1,000 it's 99.8c. At 10k it's 99.98c. Etc. It tends towards $1 the higher it goes.

Calculating the full kelly bet, someone would bet 49% of their bankroll at 1-in-100. 49.9% at 1-in-1k. 49.99% at 10k. Etc. Personally, I'm not going to bet something at full kelly, preferably closer to half kelly or maybe quarter kelly -- although generally, figuring it out is more based on the max bet a casino will tolerate and not necessarily some % of kelly, but that's beside the point.

Essentially, I'd say someone should make the bet where their bankroll is at least, bare minimum, 2 times the size of their wager (potential loss). But you would also have to update your bankroll after each wager, because in case you did have a loss, your bankroll would be significantly lower and betting again at the same price would be way overbetting. If you MUST bet 50 times at the same price, then that's obviously going to lower your max bet amount, but I don't particularly feel like figuring that out -- but my guess is it's going to be a much lower number for the lower cases (like 1-in-100, your optimal bet isn't going to be 50% or your bankroll but more like 25% I'd guess, due to the fact you have a much higher chance of losing) and it's going to be closer to 50% of BR for the higher cases like 1-in-1M, because you have such a lower chance to lose.



Using the 1-in-1k example, and I'm going to assume everyone's completely willing to do it 50 times since everyone's bankroll should be high enough to warrant that. Each wager you have a 0.999 chance to win. After 50 spins, you have a 0.999^50 = 0.9512 or 95.12% chance to win every spin. That means (roughly) you have a 19-in-20 chance of winning $100 and a 1-in-20 chance of losing. Of the losing scenarios, you're going to have most cases where you lose once for $1k and win 49 times for $98, for a net loss of $902. But some cases you're also going to lose twice at $1k and only win 48 at $2 for a net loss of $1,904... At the far left of the curve, you'll have a 1-in-10^150 chance to lose all bets for a loss of $50k. You'll see 18 yos in a row plenty of times over before you see a 50-for-50 loser, but the point remains, someone is going to lose $902 or $1,904, etc.

At 1-in-10k, there'll be about 1-in-200 people will lose at least $9,902 (or more), whereas 199-in-200 will win $100.

[monsterj]

Say you had the opportunity to pick a number between 1 and 1,000. If your number matches a pre-selected number in that range, you have to pay $1,000. However, if your number does not match (which will happen 99.9% of the time), you will get $2. Obviously this is highly +EV. Would you do it? I assume everyone on this forum would say YES.

However, let's change this to a number between 1 and 1,000,000, where if your number matches, you owe $1,000,000. If it doesn't, you get $2. Would you do it (provided you had at least $1,000,000 in assets)? I wouldn't. I bet a lot of you also wouldn't.

So it's a matter of risk/reward, obviously.

What is the highest odds number where you'd accept it? 1 in 500,000? 1 in 100,000? 1 in 20,000?

Assume that you can only do it a maximum of 50 times, and you can't pool your resources together with others.

No offense Druff, but nobody worth more than $1000 would ever enter either contest. It's stupid, and a good example of kelly gambling paradox.

[RS_]

Say you had the opportunity to pick a number between 1 and 1,000. If your number matches a pre-selected number in that range, you have to pay $1,000. However, if your number does not match (which will happen 99.9% of the time), you will get $2. Obviously this is highly +EV. Would you do it? I assume everyone on this forum would say YES.

However, let's change this to a number between 1 and 1,000,000, where if your number matches, you owe $1,000,000. If it doesn't, you get $2. Would you do it (provided you had at least $1,000,000 in assets)? I wouldn't. I bet a lot of you also wouldn't.

So it's a matter of risk/reward, obviously.

What is the highest odds number where you'd accept it? 1 in 500,000? 1 in 100,000? 1 in 20,000?

Assume that you can only do it a maximum of 50 times, and you can't pool your resources together with others.

No offense Druff, but nobody worth more than $1000 would ever enter either contest. It's stupid, and a good example of kelly gambling paradox.

What's the paradox? The "higher" you play, the lower your chance is to lose. The advantage (dollars, not percentage) is relatively unchanged as it tends towards $1.


Idk about anyone else, but if the "50 max spins" thing was removed, and this was let's say, a slot machine with the same odds, then I'd absolutely play it for $1,000. All day and all night, I would play it. Well, that's at least assuming I could get a handful of plays off per hour. Not going to waste my time playing for $20/hr or some nonsense. Not sure how high I'd go, but if this was a real life thing in front of me right now, I think I'd almost certainly do it for $5k and very likely for $10k. Higher than that, I'd probably want to do a bit more math on it -- essentially, do a random-walk sim and see what the volatility looks like "in real life", like the potential ups/downs and growth over time. But that's more due to the fact I'm probably a bit more conservative than your average bear.

[lol wow]

todge can you plz limit ur online math nerd posters from limiting scams or making them not as enticeable

[lol wow]

as a 68 year old white male u know postmates from cheesecake factory are not paying for themselves

[gimmick]

No offense Druff, but nobody worth more than $1000 would ever enter either contest. It's stupid, and a good example of kelly gambling paradox.

What's the paradox? The "higher" you play, the lower your chance is to lose. The advantage (dollars, not percentage) is relatively unchanged as it tends towards $1.


Idk about anyone else, but if the "50 max spins" thing was removed, and this was let's say, a slot machine with the same odds, then I'd absolutely play it for $1,000. All day and all night, I would play it. Well, that's at least assuming I could get a handful of plays off per hour. Not going to waste my time playing for $20/hr or some nonsense. Not sure how high I'd go, but if this was a real life thing in front of me right now, I think I'd almost certainly do it for $5k and very likely for $10k. Higher than that, I'd probably want to do a bit more math on it -- essentially, do a random-walk sim and see what the volatility looks like "in real life", like the potential ups/downs and growth over time. But that's more due to the fact I'm probably a bit more conservative than your average bear.

Very often it's not worth any ones time and when you move the numbers to a real life example where the chance of it being rigged becomes another very real variable it just doesn't look too good anymore.

When you keep making it more "favorable" by increasing what you can lose, the chance you're getting conned more than negates it.

[RS_]

What's the paradox? The "higher" you play, the lower your chance is to lose. The advantage (dollars, not percentage) is relatively unchanged as it tends towards $1.


Idk about anyone else, but if the "50 max spins" thing was removed, and this was let's say, a slot machine with the same odds, then I'd absolutely play it for $1,000. All day and all night, I would play it. Well, that's at least assuming I could get a handful of plays off per hour. Not going to waste my time playing for $20/hr or some nonsense. Not sure how high I'd go, but if this was a real life thing in front of me right now, I think I'd almost certainly do it for $5k and very likely for $10k. Higher than that, I'd probably want to do a bit more math on it -- essentially, do a random-walk sim and see what the volatility looks like "in real life", like the potential ups/downs and growth over time. But that's more due to the fact I'm probably a bit more conservative than your average bear.

Very often it's not worth any ones time and when you move the numbers to a real life example where the chance of it being rigged becomes another very real variable it just doesn't look too good anymore.

When you keep making it more "favorable" by increasing what you can lose, the chance you're getting conned more than negates it.

It's definitely an interesting math/gambling "discussion". I don't think anything exactly like this in real life would ever present itself, at least as written, but that doesn't mean it isn't useful to explore...at least for me. I like these weird "odd ball" type bets because it makes me think about things differently. It may be in a few weeks, months, or years, but there may be a situation where this type of thing may come in handy. It happens enough to make it "worth it" for me, since I'm an AP...and this is kind of my job, both figuring out how to beat known games as well as beating games that I haven't seen before. There are different scenarios all the time where thinking outside the box is the difference between beating a play vs crushing it.

The EV slightly increases as the number goes up, but the volatility grows significantly "faster" than the EV, making it not worth the increase, if you could choose between, say, 1k vs 10k, there would be no reason to choose 10k if 1k was available, since the extra $0.0018 in EV/round isn't worth that variance. I prefer the certainty of the lower number, assuming you play a somewhat significant # of rounds for both cases.

[gimmick]

Very often it's not worth any ones time and when you move the numbers to a real life example where the chance of it being rigged becomes another very real variable it just doesn't look too good anymore.

When you keep making it more "favorable" by increasing what you can lose, the chance you're getting conned more than negates it.

It's definitely an interesting math/gambling "discussion". I don't think anything exactly like this in real life would ever present itself, at least as written, but that doesn't mean it isn't useful to explore...at least for me. I like these weird "odd ball" type bets because it makes me think about things differently. It may be in a few weeks, months, or years, but there may be a situation where this type of thing may come in handy. It happens enough to make it "worth it" for me, since I'm an AP...and this is kind of my job, both figuring out how to beat known games as well as beating games that I haven't seen before. There are different scenarios all the time where thinking outside the box is the difference between beating a play vs crushing it.

The EV slightly increases as the number goes up, but the volatility grows significantly "faster" than the EV, making it not worth the increase, if you could choose between, say, 1k vs 10k, there would be no reason to choose 10k if 1k was available, since the extra $0.0018 in EV/round isn't worth that variance. I prefer the certainty of the lower number, assuming you play a somewhat significant # of rounds for both cases.

As long as it's within a theoretical model where all variables are known using full Kelly criterion is still the most efficient way to increase your bankroll. I don't think anyone uses it though. BJ players and sports bettors fairly quickly noticed that the edges weren't as high as they thought. Cheating, not getting payed or only getting action when you're losing all make a dent. Half and quarter Kelly gives you room to be wrong.

The way the numbers were in this example it would always be yes in theory and no in practice. This mostly resembled that coin flip scam where Iceman was involved. Where they offered something like 60/40 on "fair" coin flips. The guy that was flipping the coin was doing something like 30/70 flips.