At what point does arena become better value than boosters? [duplicate]

If you take a look at this answer, you'll see the break even points for gold. I'm not considering dust or cards as part of breaking even since its hard to value those:

• You have the possibility of breaking even (100g for a booster + 50g back) after just 1 win.
• You will always break even after 5+ wins (though at 4 wins its very close to break even as well).
• After 7 wins, you will be playing the arena for free as you'll get your entire gold entry fee back.

Three games is widely considered to be the break even point. The Arena costs 50 gold more, and at three wins you tend to get around 50 gold back (or a mix of gold and dust). Three wins is also the number of wins a statistically average player is likely to achieve.

You also have to consider that playing constructed would earn you 10 gold per three wins, so the actual break even point taking that into account is probably a bit higher than three wins.

I'd summarize the decision in the following way:

• If you like playing Arena, then just play it
• If you're at least an average player, you're likely to break even
• If you're a better than average player, the arena is better than buying booster packs
• If you're a great player and can achieve 7+ wins on average, you can earn boosters continously for however long you're playing Arena