Friday, December 23, 2011

Coconut Casino Explained

Since I've been farming cracked alloys, I inevitably had to decide whether I want to risk money into the coconut slot machines. But eh, 5 bars is a lot to give up (could set me back a full day) so I thought I might as well do an analysis.

First of all, this thing is definitely a scam, but some scams are actually worse than others. This is the board:



You put bets into each food item and they'll roll randomly, and if you land on a food square, it will give you back the number * the amount you bet.

i.e. you put 10 into clover and you land on clover, it'll pay out 10 * 100 = 1000 coins. You can bet max 10 in any food item, up to 10 in each for a full bet of 80 (and if it lands on any food item, you get 10 * the food's payout).

If you land on !, then you either lose (and get nothing), or you get a free spin. This is random.

If you land on ?, then you get a payout of 0, 1, 10 or 100 coins, again random.

First of all, the fundamental scam is this, you trade gold for coconut coins, which isn't worth shit unless you open a perm, but mostly you'll be getting saphaels.

Second of all, this actually operates on two fallacies that makes people with a lot of gold (or just really impatient) lose more money.

Fallacy #1: Betting 10 coins in any one food item is the same as betting 1 in that food item 10 times.
Fallacy #2: Betting 1 coin each in two food items is the same as betting 1 in one food item, then betting 1 in the other.

To understand why this is, we must first understand how much of a payout that ? square is.

Here is the data after 361 bets (actually 413 rolls because of !)

!: 133/431 = 32.20% ~ 1/3
success: 52/133 = 39.09% ~ 2/5

?: 104/413 = 25.18% ~ 1/4
0: 33/104 = 31.73% ~ 3/10
1: 40/104 = 38.46% ~ 2/5
10: 30/104 = 28.88% ~ 3/10
100: 1/104 = 0.96% ~ 1/100

Cookie: 106/413 = 25.67% ~ 1/4
Candy: 33/413 = 7.99% ~ 2/25
Chocolate: 17/413 = 4.12% ~ 1/25
lollipop: 10/413 = 2.42% ~ 1/40
kebob: 5/413 = 1.21% ~ 1/80
sundae: 5/413 = 1.21% ~ 1/80

That's right, ? accounts for 1/4th of your rolls, and it's worth 2/5 * 1 + 3/10*10 + 1/100 * 1 = 3.4 coins.

The key here is, the ? is worth 3.4 coins whether you put in 1 or 80.

In other words, if you bet 10 for one spin instead of 1 for 10 spins, you give up 9 * 3.4 = 30.6 coins.
Similarly, if you bet 1 + 1 for one spin instead of 1 for 2 spins, you'll give up 3.4 coins.

If you do the full grand slam of 80 gold in one bet, you in fact lose 79 * 3.4 = 268.6 coins. To put that in perspective, for 3x, you only need 180 coins to get the alloy.

So, the optimal bet is in fact 1 gold at a time, but where do we put it?

cookie: 106 * 2 = 212 coins
candy: 33 * 5 = 165 coins
chocolate: 17 * 10 = 170 coins
lollipop: 10 * 15 = 150 coins
kebob: 5 * 20 = 100 coins
sundae: 5 * 40 = 200 coins

So, somewhat confirming folk theory, cookie really is the best payout. Though if you're feeling adventurous, you can get decent results out of sundae. Everything else is a scam.

Finally, what's the expected return of 1 gold on cookie?

The success rate on ! is 2/15, so subtract that from 1 and we get 13/15

the payout for ? as we already know is 3.4 coins, 3.4 * 1/4 / (13/15) = 0.98 coins
cookie: 2 * 1/4 / (13/15) = 0.58 coins

add them together, and you have

0.98 + 0.58 = 1.56 coins per 1 gold, the return is 1.56, which is actually a ton higher than most casinos, but again, coins are worthless compared to gold so your loss is in fact 100%.

To illustrate, let's calculate the returns on an 80-coin bet.

the payout for ? again is 0.98 coins
cookie: 5.77 coins
candy: 50 * 2/25 / (13/15) = 4.62 coins
chocolate: 100 * 1/25 / (13/15) = 4.62 coins
lollipop: 150 * 1/40 / (13/15) = 4.33 coins
kebob: 200 * 1/80 / (13/15) = 2.88 coins
sundae: 400 * 1/80 / (13/14) = 5.77 coins

total: 0.98 + 5.77 + 4.62 + 4.62 + 4.33 + 2.88 + 5.77 = 28.97 coins per 80 gold. The return is 0.36.

For once, the sprite's "Slow and steady wins the race" advice is actually genuine.

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