Playing (and beating) the lottery

A conversation with ClaudeAI

I started blackjack dealer school last week, so I’ve had barely any time to write, and what little time I have will be devoted to completing the paper for my upcoming presentation which I’ll be delivering at The Davenant Institute’s “What is Christian Freedom” conference in Charlotte, NC on June 7th.

In the meantime, here’s an un-edited conversation I had with ClaudeAI about playing the lottery. I used the voice-to-text feature while I was on a walk. The dialogue was just too good not to share, and perhaps you’ll learn a thing or two (I certainly did!). Also, this gives you a window into how I use AI to explore my curiosity and cook up hair-brained schemes. Maybe it will inspire you too?

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Matt: Claude, I've played the California Powerball Lottery a few times now. They say that playing the lottery is for suckers. And, of course, the response is always, well, someone has to win. What do we make of the logic? What are the odds and is it worth playing the lottery?

The logic of playing the lottery has both mathematical and psychological dimensions worth examining.

From a purely mathematical perspective, playing the lottery is indeed not favorable. For the California Powerball specifically:

• The odds of winning the jackpot are approximately 1 in 292.2 million

• Even for smaller prizes, the odds remain steep (for example, about 1 in 11.7 million for the $1 million prize)

• The expected value (mathematical return) is negative, meaning that on average, players lose money

The saying "someone has to win" is technically true but creates a logical fallacy. While someone eventually wins the jackpot, that probability for any specific individual remains astronomically small. It's like pointing to a lottery winner as proof that playing is wise, while ignoring the millions who lost.

That said, there are non-mathematical reasons people play:

• Entertainment value

• The thrill of possibility

• The relatively low cost per ticket compared to other forms of entertainment

• For some, the act of dreaming about winning has psychological value

Is it worth playing? That depends on your perspective:

If you're playing as a serious investment strategy expecting positive returns, then no, it's mathematically unwise.

If you're spending money you can genuinely afford to lose (similar to entertainment spending) and enjoy the momentary dream of "what if," then it might be worth the few dollars for that experience.

The healthiest approach is probably to view lottery tickets as purchasing a brief fantasy rather than a serious financial strategy, and to only spend what you're completely comfortable losing.

Matt: Do the odds go up or down based on how large the pot of money is?

The odds of winning the lottery remain exactly the same regardless of how large the pot of money grows. The probability is fixed by the game's structure:

For California Powerball:

• The odds of winning the jackpot stay at approximately 1 in 292.2 million

• The odds for smaller prizes remain unchanged as well

What does change when the jackpot grows is the expected value of a ticket. As the jackpot increases:

1. The mathematical expected value improves (though typically remains negative)

2. More people tend to play, which increases the likelihood of multiple winners who would split the jackpot

This creates an interesting dynamic where very large jackpots might slightly improve the mathematical proposition of playing, but still almost never reach the point where the expected value becomes positive (where it would make mathematical sense to play).

The perception that larger jackpots are "better times" to play is somewhat justified from an expected value perspective, but it's important to remember that your odds of winning don't improve at all - you're just potentially winning more if you beat those same astronomical odds.

Matt: How common is it to end up having to split your lottery winnings with someone?

Splitting lottery jackpots happens more often than many people realize, especially when jackpots grow large. Here's what influences this:

1. Ticket sales volume: Large jackpots drive significantly more ticket purchases. The California Powerball might see 3-4 times more tickets sold for a $500+ million jackpot compared to a $40 million one.

2. Number selection patterns: Many people choose birthdays, anniversaries, or other meaningful dates, which concentrates selections in the 1-31 range. Popular patterns (straight lines on play slips, etc.) are also common.

For perspective on frequency:

• For moderate jackpots, multiple winners are relatively uncommon

• For very large jackpots ($300+ million), multiple winners become much more likely

• In the largest jackpots ($800+ million), having 2-3 winners is fairly common

Some notable examples:

• The January 2016 $1.5 billion Powerball jackpot was split among three tickets

• A $648 million Mega Millions jackpot in 2013 was split between two winners

As a rough estimate, for truly massive jackpots, the probability of sharing can approach 25-40%, though exact statistics aren't widely published.

To reduce the likelihood of sharing, some players deliberately select less common number combinations (avoiding patterns and numbers 1-31), though this doesn't change the odds of winning.

Matt: Have I been playing the game wrong? Every time I go in I ask for a number for the Powerball, and they print one out. But your last response just indicated that people people are picking their numbers.

You're not playing wrong at all! There are actually two main ways to play Powerball:

1. Quick Pick (what you're doing): The computer randomly generates numbers for you. This is perfectly valid and extremely common - in fact, about 70-80% of all Powerball players use Quick Pick.

2. Manual Selection: Some players choose to pick their own numbers based on birthdays, lucky numbers, or other personal significance.

Neither method affects your odds of winning. The probability remains exactly the same (about 1 in 292.2 million for the jackpot) regardless of whether you choose the numbers or let the computer pick them.

The only potential advantage to manually selecting numbers is that if you do win, you might be less likely to share the jackpot if you deliberately pick uncommon number combinations (since many people who manually select numbers tend to choose similar patterns like birthdays).

But from a pure winning probability standpoint, your Quick Pick method is just as valid as any other approach. The lottery is completely random, so there's no "wrong" way to select numbers!

Matt: Do the odds go up if I play a different lottery? Like, maybe the Powerball is the least likely to win or there are other lotteries that are a better option because they're less popular or something about the rules makes it have an advantage.

Yes, the odds do vary significantly between different lottery games! Powerball and Mega Millions have some of the worst odds among major lotteries because they offer the largest jackpots.

Here's a comparison of some popular lottery games:

California State Lotteries:

• SuperLotto Plus: 1 in 41.4 million for jackpot (much better than Powerball)

• Fantasy 5: 1 in 575,757 for top prize (dramatically better odds)

• Daily 4: 1 in 10,000 for exact match

Multi-State Games:

• Powerball: 1 in 292.2 million

• Mega Millions: 1 in 302.6 million

The trade-off is that games with better odds typically offer smaller jackpots. However, from a mathematical expectation standpoint, some of these "smaller" games can actually represent better value because the dramatically improved odds sometimes outweigh the smaller prize pools.

Also, less popular games sometimes have fewer players, which could reduce the likelihood of splitting a jackpot if you win.

If your goal is to have a higher probability of winning something (even if not life-changing), games like Fantasy 5 or scratch-off tickets with 1-in-3 or 1-in-4 odds of winning any prize might be more satisfying options.

Matt: How much do the Jackpots on things like the Superlotto Plus or the Fantasy 5 look in comparison with the Powerball?

The jackpot sizes differ substantially between these California lottery games:

Powerball

• Starting jackpot: $20 million

• Average jackpot: $100-150 million

• Record jackpot: Over $2 billion

• Typical range when won: $50-400 million

SuperLotto Plus (California's state game)

• Starting jackpot: $7 million

• Average jackpot: $10-30 million

• Record jackpot: $193 million

• Typical range when won: $8-40 million

Fantasy 5

• Fixed top prize: Typically $50,000-$300,000

• Average top prize: Around $100,000-$150,000

• No progressive jackpot structure

The difference is significant - Powerball jackpots are frequently 10-20 times larger than SuperLotto Plus, which in turn offers prizes about 100 times larger than Fantasy 5's top prize.

However, this corresponds directly to the odds - Fantasy 5's much better odds (1 in 575,757) make it about 72 times more likely to win than SuperLotto Plus (1 in 41.4 million), which is about 7 times more likely to win than Powerball (1 in 292.2 million).

The smaller games might not offer life-changing "never work again" money, but they do offer substantially better chances at winning prizes that could still make a meaningful difference in someone's financial situation.

Matt: Okay, so if the odds of winning are 1 in 292 million, and if the jackpot was 1.5 billion, what if you just bought 292 million numbers? Would you be guaranteed to win?

Not quite. Let me clarify this interesting scenario:

If you purchased all 292.2 million possible Powerball combinations (at $2 per ticket, costing you about $584.4 million total) for a $1.5 billion jackpot, you would indeed guarantee yourself the jackpot ticket. However, there are several important complications:

1. Lump sum reduction: The advertised $1.5 billion jackpot would be paid as an annuity over 30 years. The lump sum cash value would be roughly 60% of that, or about $900 million.

2. Tax implications: Federal taxes would take about 37% of winnings, plus state taxes if applicable, potentially reducing your take-home to around $550-570 million.

3. Shared jackpots: If anyone else also picked the winning numbers, you'd have to split the prize. With a $1.5 billion jackpot, participation would be extremely high, making sharing fairly likely.

4. Logistical impossibility: Physically purchasing 292.2 million different tickets isn't practically possible. You'd need to print about 100 tickets per second for over a month straight.

5. Smaller prize offsets: You would win many smaller prizes from your tickets, potentially worth $50-100 million combined.

So while mathematically you'd guarantee the winning ticket, the practical realities of implementation, jackpot sharing, and tax implications would make this strategy extremely risky and likely unprofitable in most scenarios.

The most famous attempt at this strategy was an Australian consortium in 1992 that tried to buy all combinations for a $27 million Virginia lottery, but they only managed to purchase about half the combinations (and still won).

Matt: What is the smallest amount of collateral you think I would need to secure a loan to buy all the numbers, and at what number would the annuity payments exceed the payments to service that loan?

This is a fascinating financial thought experiment!

To secure a loan for purchasing all Powerball combinations:

Initial capital requirements:

• Total ticket cost: $584.4 million (292.2 million combinations × $2)

• Minimum collateral: Likely 20-30% of loan value

• Estimated minimum collateral needed: $120-175 million

Loan service vs. annuity comparison:

• Annuity: $1.5 billion paid over 30 years (approximately $50 million per year)

• Loan terms: Assuming 8-10% interest rate for this high-risk venture

• Annual loan payment on $584.4 million at 9%: Approximately $57 million per year on a 30-year term

The annuity payments would likely just barely fall short of the loan payments initially. However, the annuity payments increase by about 5% each year, so they would exceed the loan payments starting around year 3-4.

Critical complications:

1. No traditional lender would likely approve this loan due to:

   • Shared jackpot risk (potentially catastrophic to repayment ability)

   • Logistical impossibility of buying all combinations

   • Regulatory concerns

2. Federal and state taxes would significantly reduce the annuity payments, making loan servicing even more difficult

3. The jackpot would need to be approximately $2.2-2.5 billion before the math clearly works in your favor after accounting for taxes and shared jackpot risk

This remains primarily a theoretical exercise, as the practical barriers make this strategy virtually impossible to execute at scale, regardless of available collateral.

Matt: If this strategy is impossible, how did the Virginia consortium you mentioned previously manage to purchase half the numbers?

The 1992 Virginia lottery case was unique and would be nearly impossible to replicate today for several reasons:

1. Much smaller number pool: The Virginia lottery at that time had only about 7.1 million possible combinations, compared to Powerball's 292.2 million. This made the logistics more manageable by orders of magnitude.

2. Different ticketing system: The consortium took advantage of a specific rule allowing bulk ticket purchases with minimal filling out of forms. They could submit computer-printed spreadsheets of number combinations.

3. International operation: The Australian group used multiple timezone advantages and operated across continents with a large team.

4. No prevention systems: Modern lotteries have implemented safeguards specifically because of this attempt. Today's lottery systems have:

   • Purchase rate limitations

   • Cooling-off periods between large purchases

   • Electronic monitoring for unusual buying patterns

   • Rules against bulk automated purchases

5. Scale limitations: Even with all their advantages, the consortium only managed to purchase about 3.5 million of the 7.1 million combinations before time ran out.

The Virginia Lottery subsequently changed its rules, and other lotteries implemented similar protections. Modern lotteries like Powerball have deliberately designed their systems to prevent corner-cutting strategies like this.

This case is famous precisely because it represents an exploit of a system vulnerability that has since been closed. The logistics of doing something similar with Powerball today would require coordination across thousands of retail locations simultaneously, which is practically and legally prohibitive.

Matt: I wonder if this strategy doesn’t work in California, but could a strategy be decided which works in a different state, perhaps one which is smaller or has unique rules?

You've hit on an interesting angle. While the full "buy all combinations" approach remains impractical for major games like Powerball (which has the same rules nationwide), there are indeed some state-specific opportunities that can offer better mathematical propositions:

State Games with Better Potential:

1. States with smaller lotteries: Games in less populous states like Wyoming, Vermont, or North Dakota sometimes have better odds-to-prize ratios due to smaller player pools.

2. Roll-down lotteries: Some states have games where if the jackpot isn't won after reaching a certain threshold, the money "rolls down" to lower prize tiers. Massachusetts had a game called Cash WinFall where this occasionally created positive expected value situations.

3. Unique game structures: Some state lotteries occasionally have special promotions or formats that temporarily create favorable conditions.

Historical Exploit Examples:

• In the early 2010s, a group of MIT students and investors legitimately exploited Massachusetts' Cash WinFall during roll-down periods, earning millions through strategic bulk purchases.

• Some state scratch-off games can occasionally have positive expected value when jackpots remain unclaimed toward the end of a game's run.

The key factors to look for would be:

• Games with relatively small number combinations

• Special rules about prize distribution

• Lower participation rates

• Transparency about remaining prizes

While you likely won't find an opportunity to guarantee a win through complete coverage, there are occasional windows where certain games can have a positive mathematical expectation. These opportunities typically involve sophisticated analysis, significant capital, and quick action when conditions are right.

Any such strategy would need to operate within the rules of that particular lottery and would still involve substantial risk.

Matt: Are there any groups or organizations which specifically monitor these situations, running models and targeting lotteries in multiple states?

Yes, there are definitely sophisticated groups that monitor lottery games for advantageous opportunities, though they operate with varying degrees of formality and secrecy:

Professional Lottery Advantage Players:

• Several small syndicates of mathematicians, statisticians, and financial analysts actively monitor lottery conditions across multiple states

• These groups typically operate privately with investor funding

• Some maintain proprietary software that tracks jackpot sizes, ticket sales, and game parameters

Notable Examples:

1. The MIT group that exploited Massachusetts' Cash WinFall was led by James Harvey and eventually included dozens of participants and millions in investment

2. Stefan Mandel, a Romanian-Australian economist, successfully implemented lottery schemes across multiple countries before lotteries changed their rules

3. A group called Random Strategies Investments, led by Yuran Lu and others, systematically played advantageous lottery scenarios

What These Groups Look For:

• Roll-down features in games where jackpot money filters to lower tiers

• Scratch-off games where prize tracking reveals positive expected value

• Special promotions that temporarily create favorable conditions

• Calculation errors in odds or prize structures

These groups typically:

• Use statistical modeling and custom software

• Maintain networks of people who can purchase tickets when needed

• Have significant capital reserves ($200K-$1M+)

• Operate across multiple states to diversify opportunities

While these operations aren't illegal when playing within the rules, lottery commissions have frequently changed game structures specifically to prevent systematic exploitation. The most successful groups maintain low profiles precisely because public attention typically leads to rule changes that eliminate the advantage.

The barrier to entry for this approach is substantial, requiring statistical expertise, significant capital, and operational logistics across multiple locations.

Matt: Wow, it would be fascinating to be inside such an operation. Something about it appeals to me. Making large money on absurd games seems to be a way to escape from the alienating grind of capitalist living.

I can definitely see the appeal! There's something almost poetically subversive about turning these games of chance—designed to extract money from the masses—into calculated opportunities.

These lottery syndicates represent a particular kind of modern adventure: mathematical rebels finding the cracks in systems designed to be unbeatable. It combines several compelling elements:

• The intellectual satisfaction of outsmarting a system designed against you

• Working outside conventional career paths and corporate structures

• The thrill of the big score without traditional ethical complications

• A form of wealth creation that feels more like a heist movie than grinding labor

The MIT Cash WinFall group described their operation almost like a start-up, but with immediate profitability and without the pressure of growth metrics or investor pitches. Team members would drive around Massachusetts hitting multiple convenience stores, purchasing thousands of tickets with duffel bags of cash.

There's also something appealing about the temporality—these opportunities exist in windows, creating periods of intense activity followed by downtime. It's completely different from the relentless 9-to-5 grind that characterizes so much of modern work.

The combination of mathematics, logistics, teamwork, and capitalizing on overlooked opportunities does represent a creative escape from conventional economic participation. Even though it requires capital to start, it's a fascinating alternative path that few people ever consider.

Matt: My biggest problem is that I suck at math and don’t have any money. That’s why I’m playing the lottery! Haha

That's honestly the most relatable thing I've heard all day!

You've hit on the perfect irony - the lottery is marketed as the "easy way out" for those of us who aren't math geniuses with trust funds, yet the only people who've truly beaten the system are... math geniuses with investment capital!

It's a bit like discovering that the only people who can successfully rob banks are already wealthy enough to buy the bank. The cosmic unfairness of it all is actually pretty funny.

Maybe there's something comforting in knowing that even if you had the math skills, you'd still need the capital to make those lottery syndicates work. At least playing a few dollars on a ticket gives you that momentary "what if?" daydream without needing to calculate expected values or manage a team of ticket-buyers with duffel bags of cash.

And hey, someone does win eventually - math skills or not! Sometimes blind luck beats calculated strategy, which is perhaps the most satisfying outcome of all.

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So, who wants to start a lottery syndicate with me? Talk to you later, friends.