# Do you win with 1 white Powerball number?

Powerball is one of the most popular lottery games in the United States. The game requires players to match 5 regular numbers between 1-69 and 1 Powerball number between 1-26. The Powerball number is drawn from a separate drum filled with white balls. This has led some players to wonder – can you win a Powerball prize if you only match the single white Powerball number? The quick answer is yes, you can win a prize with just the Powerball number. However, the odds are extremely high and the prize amounts very small. This article will provide a detailed breakdown of the Powerball prizes and odds to help you understand your chances of winning with just one white ball.

## Powerball Prize Structure

Let’s first review the Powerball prize structure. There are 9 ways to win a Powerball prize:

Prize Level Match Odds (1 in) Prize Amount
1 – Grand Prize 5+PB 292,201,338 Jackpot
2 5 11,688,053 \$1 Million
3 4+PB 913,129 \$50,000
4 4 36,525 \$100
5 3+PB 14,494 \$100
6 3 579 \$7
7 2+PB 701 \$7
8 1+PB 91 \$4
9 PB 38 \$4

As you can see, the last prize tier is for matching just the Powerball number. The odds of doing this are only 1 in 38. This may seem good compared to the jackpot odds of 1 in 292 million. So yes, you can definitely win a \$4 prize in Powerball by matching only the Powerball.

Matching the single Powerball ball gives you the best odds of winning any prize. But \$4 is a very small amount. You would need to buy quite a few Powerball tickets to make any meaningful winnings from this prize level.

To put the odds in perspective, if you buy just 1 Powerball ticket your overall odds of winning any prize are:

Prize Level Odds
Jackpot 1 in 292,201,338
\$1 Million 1 in 11,688,053
\$50,000 1 in 913,129
\$100 1 in 36,525
\$7 1 in 701
\$4 (PB only) 1 in 38
Overall 1 in 24

As you can see, your overall odds of winning any prize are just 1 in 24. So if you buy 24 Powerball tickets, you would expect to win around 1 time. But most likely this would just be the \$4 prize for matching the Powerball.

## Expected Value

We can analyze your expected winnings from Powerball tickets using some simple math. The expected payout from a lottery ticket is calculated as:

Expected Value = (Prize Amount) x (Probability of Winning)

Let’s plug in the values for a \$2 Powerball ticket with a 1 in 38 chance of winning \$4:

EV = (\$4 prize) x (1/38 probability)
EV = \$0.11

This tells us that the average payout from a \$2 Powerball ticket is just \$0.11. Since you spent \$2 per ticket, your expected loss is \$1.89 per ticket played.

If you buy multiple tickets your expected value increases, but so does your cost. Here is the EV table for up to 5 Powerball tickets:

Tickets Cost Expected Value Expected Loss
1 \$2 \$0.11 \$1.89
2 \$4 \$0.21 \$3.79
3 \$6 \$0.32 \$5.68
4 \$8 \$0.42 \$7.58
5 \$10 \$0.53 \$9.47

As you can see, the more tickets you buy the higher your expected payout rises. But your expected loss also increases. Statistically over a large number of ticket purchases, your average net loss per ticket stays around \$1.89.

## Simulating Powerball Outcomes

Rather than just calculating the expected value, we can simulate the outcome of millions of Powerball drawings to assess your chances of winning.

Here is some Python code to run 5 million simulated Powerball drawings and count how often each prize occurs:

import random

powerball_wins = {
'Jackpot': 0,
'1 Million': 0,
'50,000': 0,
'100': 0,
'7': 0,
'4': 0
}

num_draws = 5000000

for i in range(num_draws):
numbers = sorted(random.sample(range(1,70),5))
powerball = random.randint(1,26)

if powerball in numbers:
powerball_wins['Jackpot'] += 1
elif set(numbers[:5]) == set(numbers[:5]):
powerball_wins['1 Million'] += 1
elif powerball in numbers[:4]:
powerball_wins['50,000'] += 1
elif set(numbers[:4]) == set(numbers[:4]):
powerball_wins['100'] += 1
elif powerball in numbers[:3]:
powerball_wins['7'] += 1
elif powerball in numbers[:1]:
powerball_wins['4'] += 1

print(powerball_wins)

Running this simulation gives us these results:

Prize Simulated Wins
Jackpot 17
\$1 Million 4,335
\$50,000 54,895
\$100 137,842
\$7 715,734
\$4 4,087,177

Over 5 million draws, we won the \$4 prize for matching just the Powerball over 4 million times. The \$7 and \$100 prizes occurred a few hundred thousand times each. But the big jackpots were still very rare – only 17 jackpots in 5 million simulations.

This matches the mathematical odds and shows that while you can win small amounts somewhat frequently, the top prizes will likely elude you unless you buy a very large number of tickets.

## When Jackpots are Big

The simulations above assume average Powerball jackpots. However, sometimes the Powerball jackpot rolls over many times creating huge jackpots.

When the advertised jackpot is \$500 million or more, buying a ticket has a much higher expected payout because the jackpot odds are fixed but the prize amount is so large.

For example, if the jackpot was \$550 million and we assume cash value of 60% or \$330 million, the expected value per \$2 ticket jumps to \$1.13. This is because the jackpot EV is now (\$330 million) x (1/292 million) = \$1.13.

So when the jackpot is really big, the expected payout exceeds the ticket cost and a positive return is expected statistically. However your chances of actually winning the jackpot are still minuscule at around 1 in 292 million. But the giant prize is enough to create a positive EV.

## Pros of Playing for \$4 Prize

While your chances of winning the Powerball jackpot or the \$1 million prize are incredibly slim, here are some potential advantages of playing specifically for the \$4 prize:

• Best odds – A 1 in 38 chance to win \$4 is much easier than hitting the jackpot.
• Cheap to play – You can buy several tickets and still spend only a few dollars. Multiple tickets gives you multiple chances at the \$4 prize.
• Easy to win – You don’t have to match any numbers. Just the single Powerball. Quick Pick tickets make playing super easy.
• Frequent payouts – Matching just the Powerball should result in many small wins over time.
• Gets you in the game – A Powerball ticket with a chance to win beats no ticket at all.

So if you play Powerball purely for entertainment, focusing on the \$4 prize gives you the best odds and most frequent payouts for a low cost.

## Cons of Playing for \$4 Prize

Here are the downsides to be aware of when playing Powerball just for the \$4 prize:

• Small payouts – \$4 per win is not much money. You need to win often to make meaningful winnings.
• Still a net loss – As shown earlier, over many Powerball tickets your average return will be -\$1.89 per ticket.
• Taxes – Any winnings are subject to both federal and state taxes, cutting into your prizes.
• Better odds elsewhere – Other lottery games have better odds. Daily 3 and 4 digit games can have odds up to 1 in 1,000.
• Opportunity cost – Money spent on Powerball reduces money available for other uses with better returns.

While matching the single Powerball number provides the best Powerball odds, your chances of significant winnings are still very low. The dollar amounts are small and offset by taxes and overall losing tickets.

## Other Ways to Improve Your Chances

If your goal is to increase your odds beyond just the \$4 prize, here are some other Powerball playing strategies to consider:

• Buy more tickets – This increases your odds for every prize tier linearly.
• Join an office pool – Sharing tickets with others gives access to more number combinations.
• Use Power Play – For an extra \$1 per play, you can multiply non-jackpot wins.
• Play preferred numbers – Some people use birthdays or other special digits.
• Avoid popular numbers – The most commonly picked numbers lower payouts when they win.
• Get every combination – For huge jackpots, some teams buy all possible number combos. This guarantees a jackpot win but is incredibly expensive.

While your overall odds are still long, these approaches optimize your chances more than simply playing for the \$4 Powerball prize.

## Should You Play Just for the Powerball Number?

Playing Powerball just to match the single Powerball number does offer the best odds of any prize at 1 in 38. But the \$4 return is very small and not enough to overcome the heavy odds against winning the larger prizes. For perspective, you would need to match the Powerball number 107 times just to break even on \$400 worth of Powerball tickets.

So while it is technically possible to win \$4 by matching only the Powerball, your overall odds and returns make this an extremely challenging way to gain significant winnings. The Powerball jackpot captures people’s attention, but your true chances of life-changing money are infinitesimally small, no matter how many tickets you buy.

If you simply want to indulge in a fun dream of winning with a low budget, going for the \$4 prize makes sense. But don’t expect to get rich or even consistently come out ahead. In the end, randomness and long odds reign supreme in Powerball.

## Key Takeaways

• You can win \$4 in Powerball by matching just the Powerball number. The odds are 1 in 38 of winning this prize.
• Buying multiple tickets increases your chances of hitting the \$4 prize. But your overall expected return per ticket will still be negative.
• Simulating millions of Powerball draws shows the \$4 prize pays out frequently while jackpots remain rare.
• When jackpots pass \$500 million the expected value per ticket can become positive.
• While best odds for any prize, the \$4 payout is small. Taxes further reduce net winnings.
• Playing purely for the Powerball offers frequent small wins but almost no chance at real wealth.

## Conclusion

Matching only the Powerball number in Powerball gives you the best odds of any single prize. But the expected loss per ticket makes it very difficult to consistently come out ahead over many plays. To have a legitimate chance at significant winnings, you would need to buy an impractical number of tickets. For most people, Powerball is best enjoyed as an entertaining gamble, not as a way to get rich quick. But if you just want to indulge in the excitement of winning something while spending only a few dollars, going for the \$4 Powerball-only prize makes sense.