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10-19-2009   #1 (permalink)
tommmmmm
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Join Date: Feb 2009
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Lightbulb [Guide] Slime Races - all you need to know.

Elaborate on slime races;

Notice: Because the majority of the Lunia community simply doesn't like complicated math, I'll skip those parts and some almost-non-relevant parts too. I'll also represent the numbers rounded maximum to one point after coma.

As we all know by the law of matematics you'll loose all your money in the end, with exactly 2.7% rate of loss each race (called `House` advantage), however the purpose of this elaborate is to minimase that chance to the levels of it happening once per lifetime. The intuition suggests that it will require huuuge amounts of gold. Will it really? Let's look closer.

Because the probability distribution is "normal" (which means all cases are equally probable) every betting strategy is homomoprhic with another in one way or the other. So let's focus on one thing we can minimise - time.

I'll explain it by examples:

Example 1:
You bet 1g on green slime. After 34 runs you start betting 2g. After another 34 runs you start betting 4g - and so long. On average (I mean mathematical average) you need to wait 35 runs to earn 1g. With a standard deviation of 35 you can wait really long till you win. Let as asume that there are 12 runs per hour (5min per run including the race itself - that is very good approximation). That means you need to wait 2 hours 55min to earn 1g. On average.

Example 2:
You bet 1g on red. If not succeded you bet twice the previous amount. In this case you'll loose 6 times per hour and win 6 times per hour. Which gives 6g per hour.

Example 3:
You bet 1g on every lime except for green one and one of your choice. That makes 7g total. After failure you bet 7 times more than the previous bet. The probability of loosing one run is 1/8 which gives ~10.3 successes in an hour. On average. You earned 10g 30s.

Is there a method to get more successes per hour than example 3? No. Basically because other available options (high/low, red/black, etc) can be represented by some combination of bets on single limes. You also can't bet on 8 limes at once because the reward rate is 8:1 so you would basically gain nothing.
The example no. 3 is the fastest way to gain money - assuming that you have infinite amount of money (I wrote at the beginning that you'll loose your money at the end).

L Roger gives 250g per hour (if you do it well, got apropriate character, use glitches that are still left, make dimlies out of stones, etc). What is the base amount of gold bet that is needed to gain 250g in an hour, using method 3? Simple division 250 / 10,3 = 24,3g Let's make it 25 for the next paragraph.

Example how it works:
1. you bet 25g on each of 7 limes of your choice
2. if succeeded smile and go back to point 1, if not bet 175g (175=7*25) on each of 7 limes of your choice
3. if succeeded smile and go back to point 1, if not bet 1225g (7*175) on each of 7 limes of your choice

At this step you need total of 7*25 + 7*7*25 + 7*7*7*25 = 9975g
Probability of failing 3 steps of this method is 1/8 * 1/8 * 1/8 = 1/512

Moreover, you can't bet more than 10kg on each lime - so there is only one more step available with 8575g on each lime. That is impossible for most of the Lunia Community. After step 4 you're... done for good. In most cases after step 3 you're done for.

It might sound that method from example no. 2 is better. Let's speed up the equations a bit this time. You need 250/6 = 42g as a base bet to win 250g an hour. Probability of failing 9 times method no 2. is the same - 1/512. It requires 42 * ( 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 +512) which is 42 996g

Now let's stop for a second and make some conclusions and comparisons.
Pros of Method no. 3
- If you want to make the same amount of gold per hour you need to spend a lot more gold by playing with method no. 2 that playing with method no. 3.
- Method no. 3 is also much faster than no. 2 - according to the amount of successes per hour.

Pros of Method no. 2
- The increase of gold put in case of failure is low. Usually a player can fail method no. 2 even 6-7 times before going broke, while method no. 3 will make you broke in 2 tries.
- Casual player can't affor step 3 of method no. 3. - failing method no. 3 just two times happens 1/8 * 1/8 = 1/64 of cases. Which happens drastically more often than in similiar (I mean amount of gold-spent similarity) case with method no 2.

Very short conclusion: play method no. 2 for fun and method no. 3 for real gold gain.

The real gain statement was a bit of exaggeration. Even with step 4 of method no. 3 you will fail at a rate of 1/4096 which is 4096/(12*24)=4096/288=14,1 days - so even if you're icnredibly rich you'll loose all the money in 14 days of constant gambling 24/7.

if you got as far as here in this elaborate, you can read one more paragraph. This paragraph is about the fact that each run has constant probability. You just log onto sq 4 and you see that red won 15 times in a row. Will you bet black now? Then you'll loose. Each single run has the same probability of red winning - 1/2. The history of previous runs does not affect future runs. That is the law of mathematics.

more to come in due time.

Last edited by tommmmmm; 10-19-2009 at 09:41 AM.