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I have carefully tracked in Excel what slingshots and hats my opponents have. There is *NO* correlation to match selection. Matches are chosen very specifically to match your level, and to match you and your opponent by starting base level (i.e. sum of all the digits on your bird cards)… and the slings and hats appear to be random after that.
For example, when you are starting a streak, you will always have a 6, 7 or 8 multiplier advantage…. but I’ve faced a range of slings (from wood to silver, against my gold), and a range of hat points difference (from them being up one to me being up 7).
On a streak of one, the same is true, but your base advantage will be 4 or 5.
On a streak of 3, it is a stark jump — you’ll be at a base DISADVANTAGE of 13 or 14… but you can still enjoy a random hat or sling advantage. And so on.
Note that Rovio tweaks the matchup logic frequently — this spreadsheet has been steady for two weeks now, but it could change if some players are running away with it, or people are too frustrated because they can’t win.
As to whether it is best to buy cowboy hats if you don’t have complete sets of party, crown and street hats, it is CLEARLY mathematically superior to buy complete sets of the 100 pearl hats before embarking on cowboy hats.
If you buy all three lower sets, you’ll spend 1710 pearls (IIRC, party hats were 30 — it’s been a while). This will gain you a net increase of:
Gold sling = 3X on all 7 birds — +21
Wearing a crown or street hat = 2X on all 7 birds — +14
Note that this is how you MUST think about matchups when choosing spells. You compute your base + all multipliers from hats, and each sling upgrade is +7. Do the same for your opponent, guesstimating their sling based on the hats they are wearing. (I just LOOOOOVE seeing an opponent with a cowboy hat and 6 party hats, as I know I have a +14 advantage immediately, my gold sling over their bronze).
Thus, for 1710 pearls, you got 35 multipliers, paying an average of just under 50 pearls per multiplier.
If instead you go for cowboy hats, you’ll pay 500 pearls for a single 3X multiplier, or three times as much — 165 pearls each. When you FINALLY complete your cowboy set for 3500 pearls (twice as much as three lower complete sets), you’ll have +28 multipliers (3X per bird from the hats, and a bronze sling)…. and you’ll have paid 125 pearls each for them.
Yes, it takes longer to complete a set, but a set is FAR more powerful than a cowboy hat, and a much better value.
Jester
One complete set of crowns costs you 700 pearls, and gives you SEVEN multipliers — every bird you sling goes up by one. That’s a cost of 100 per multiplier on the sling. Discounting that there’s no bird advantage between crown and street, let’s say you buy cowboy hats instead, leaving sets incomplete. You pay 500 for a single 3X multiplier