Dwarf Alchemists - Crunching the Numbers [Long][Stats]

[silverback_guerilla]

I've just been analysing the rules for the Dwarf Alchemist. At first glance, he might seem pretty pointless - not nearly as good as a regular Wizard.

I have come to the conclusion that a Dwarf team should hire an alchemist for every single game.

An alchemist costs 30,000 gc to hire. At the end of the game I get 1d6 x 10,000 gc back. This is a pretty straightforward gambling bet. To determine my mathematical expectation, I add up what I win for each possible result and divide it by the number of results:

(1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5

So my expectation is 35,000 gold. A good gambler will recognise this as a good bet, since my expectation is higher than the amount I am betting. If I make this bet often enough, statistics predict that my winnings should equal 5,000 gc per bet made.

OK, so it's a good bet. But I need to have at least 30,000 gc at the beginning of each game in my treasury to make the bet. How much money should I put to one side to ensure that I always have enough gold to make the bet?

30,000 is too little: one losing bet and I am ruined, and can't continue the game. I need enough to weather the worst losing run I can expect.

My gambler's intuition says 60,000 gc is enough. A bit of experimentation confirms this. On the other hand, I can buy 6 FF for the same amount, and 6 FF = about 20,000 fans attending the game on average. Looking at the Income table shows that each 20,000 fans attending gets me a +1 on the roll, or an extra 10,000gc's per game. It doesn't look like such a good investment now - the 60,000 gold crowns could be better spend on Fan Factor.

BUT then an idea struck me: The number of fans attending the match is dependent on BOTH TEAMS' fan factor. If I have FF 5 and my opponent FF 1, we both get +1 on the roll on average, even though I have spent $50K and he has spent $10K!

If my opponent takes the obligatory 9FF and I take 3 FF and a "gambling bank" of 60,000, my match winnings will on average exceed his. We'll have a combined FF of 12 for an average extra 20,000gc/match. The Dwarves then get a further 5,000, on average. My low Fan Factor hurts him worse than it hurts me.

I rather like this idea from a fluff point of view: dwarves are notoriously tight-fisted. Why spend money attracting fans to the game if half their gate goes into his pocket? As Terry Pratchett wrote, "Dwarves don't love gold. We just say that to get it into bed."

[Darkson]

Interesting post. Our dwarf coach never took the alchemist as he didn't like the odds.

The only problem I see with your post is can you afford the envitable losing streak? If it comes after you've gained a few times, great, but if you lose often and early you could serously hamper your team development.

[silverback_guerilla]

The probability of getting any result less than break even on a particular bet (one or two on the die) is 1/3rd. The probability of rolling four such results in a row is a little more than one percent... Yes, it is a risk. But it's a fairly safe bet.

If you want to be a bit safer increase the "bank" to 70,000, or alternatively start with a slightly higher FF, and wait until you have extra cash. Once your team has developed that much, you may not need extra dough.

Investing in Fan Factor can be risky too, since you can lose FF every time you lose a game. If you lose or draw (our league doesn't play overtime except for semifinals and finals) and roll a few ones in a row... There's a lot more variables with FF, so it's hard to analyse, but I think that it's about the same.

Another thing I forgot to mention: The Alchemist is not affected by high FF. If you buy 9 FF, and it goes up a few times, it becomes more likely to drop down to the 9 to 11 level. If you start with FF 3, the worst it can go to is 1, and the sky's the limit

[Mestari]

The alchemist, as shown above, is a simple lottery machine that should give you more than it takes in the long run.
So in that sense you can call it useful. However, the alchemist is still a pretty useless rule, and several Runesmith rules suggestions (by (IIRC) Thadrin and me myself for example) have been made and every single one of them is better than the alchemist.

[silverback_guerilla]

I have seen some of the Runesmith suggestions, and they do seem more flavourful.

I don't agree that he's useless - hiring an Alchemist every game over the course of a season would seem to be about as useful as hiring a wizard for critical games during the same season. You could easily have and extra $50K after 10 games, enough for a "free" Apothecary, and in the meantime your low(er) FF has been sucking money out of the treasuries of your opponents. It's not how much gold you have, it's how much more you have.

One of the things I don't like about the Runesmith suggestions I have seen is that the advantage gained is unpredictable - you could be burning $50K for no use, if you roll a result that doesn't help your team. When hiring a Wizard, Alchemist, Necromancer or Master Chef you have a good idea what you're getting, and can plan in advance whether how you'll use it.

Interesting discussion though... thanks to everyone for your thoughts. This is just theory at the moment. I probably should put it into practice and report back to you on my results!

I will be playing in the WargamerAU league, which limits starting teams to a FF of 3 and a starting team budget of 1,200,000. With enough money to "prime the pump" and little coming in from gate attendances for any team, this could turn out to be an even better "secret weapon" than the death roller!

[Mestari]

The problem is:
-Dwarves have high AV-> low attrition
-Dwarves have low AG-> gain SPP's slowly ->low player turnover
-Dwarves have low TRR cost

The result is:
After a while, you won't need that money too much. Still, I perfectly agree that when in need of money, the alchemist is a good bet as you're expected to win more than lose.

[Darkson]

The probability of getting any result less than break even on a particular bet (one or two on the die) is 1/3rd. The probability of rolling four such results in a row is a little more than one percent... Yes, it is a risk. But it's a fairly safe bet.

Ah, but you've never met our Dwarf player. 40K,WfB, Necro, Mordheim - brilliant dice rolling. Stick him on a BB pitch, BAM, '1's here, there and everywhere.

[High & Mighty]

The probability of getting any result less than break even on a particular bet (one or two on the die) is 1/3rd. The probability of rolling four such results in a row is a little more than one percent... Yes, it is a risk. But it's a fairly safe bet.

Seriously, there's been WAAAAAAAAAYYY too much math flying around this board this week. A comment though. In order for your game to work, you need to maintain a warchest of cash in case you lose. You said 60-70k. But this means that your team rating is 6-7 points higher than it otherwise would be.

This has two implications. First, those 6-7 points may be enough to swing a handicap roll against you in a few games (which if it caused you to lose would cost you -10k in winnings).

Second, if you happened to have, say, 197 TR and then save up 60-70k so you can play the game, you've now broken into the next TR level and lose -10k earnings, so you are gambling to win 5k and paying the definite cost of -10k so in that case, it would be a bad bet.

Plus, I'd have to agree compared to wizards and runesmiths, the alchemist is pretty boring.

[Remco]

And one critical note on the statistics: The average die roll will only have the 3,5 average on the long run. Statistics determine that you'll need around 100 rolls to get such an average. That means that one bad luck streak could leave you dry on cash, and those odds aren't that slim. I worked as a waiter in a casino for a while, and you'd be surprised how many times an eight red (or black) roll takes place.

My point is: statistics only work in the long run, you shouldn't rely on them in the short run.

[Zombie]

This is an answer to the original post.

It doesn't look like you're very good in math. The first sign is that you had to add up numbers to figure out that you win 5k per game on average with the alchemist. This should have been so obvious that no caculation was needed. Everybody knows that the average on a D6 is 3.5.

The problem is the following. Your argument only makes sense if there are 2 teams in the league (if we can call that a league). If you're not always playing against the same team, it always pays off to have a higher FF.

For example, let's assume that there are 6 teams in the league. Obviously, the more teams there are, the more my argument holds true. Let's say you play against each team twice. Starting with 3 FF instead of 9 means that you'll make 10k less in each of your 10 games, while the other teams will only make 10k less in 2 of their 10 games (the 2 games they play against you).

It's not even true that starting with 6 fewer FF will give you 5k more per match from the alchemist. It will only do so for the first game. After that, you'd have enough money to hire him anyway just from the money you made from the gate. You'll probably have your 60k buffer after only one game, and will certainly have your 30k to hire him in any case.

Another problem in your reasoning is that you assume that the team makes no money from any revenue other than the alchemist. That's clearly not true. This alters the size of the buffer required. Assuming you make at least 20k every game from normal winnings alone (which you should if you start with 9 FF), then the required buffer is zero (you'll get at least another 10k each game from the alchemist). You see, starting with higher FF even helps you in this department. Since you don't need to keep any buffer at all, your team rating isn't needlessly inflated by money sleeping in your treasury.

The bottom line is that you should start with 9 FF, <i><b>especially</b></i> with dwarves to insure you can hire the alchemist every game. Don't keep any unnecessary buffer, but still hire the alchemist every game.

[silverback_guerilla]

It doesn't look like you're very good in math. The first sign is that you had to add up numbers to figure out that you win 5k per game on average with the alchemist. This should have been so obvious that no caculation was needed. Everybody knows that the average on a D6 is 3.5.

Believe me, NOT everybody knows that the average on a D6 is 3.5. At least, not on many of the message boards I frequent. The working was intended to show how I arrived at that conclusion, for the benefit of the reader. I expected more sophisticated readers to skip it.

I've been interested in gambling for a while, and I immediately recognised the Dwarf Alchemist as a simple gambling game. I was looking at it as if I were a gambler who was playing this game in a casino against the "house", and yes, it does assume that there is no other source of income, or more than two players in the league. As you point out, that's an oversimplification.

[Mestari]

It doesn't look like you're very good in math. The first sign is that you had to add up numbers to figure out that you win 5k per game on average with the alchemist. This should have been so obvious that no caculation was needed. Everybody knows that the average on a D6 is 3.5.

What I found amusing was the "Crunching the numbers[long][maths]"-part in the thread topic... an average thread around here must have more maths and longer posts than this thread has.

To sum up,
Alchemist is a good way of slightly increasing the amount of money you have, but (as Zombie has shown above) it cannot replace a high FF in any way and the "leeching"-part really doesn't work.

[Zombie]

What I found amusing was the "Crunching the numbers[long][maths]"-part in the thread topic... an average thread around here must have more maths and longer posts than this thread has.

Same here. I was quite disappointed to see so little :-)

I guess i didn't understand the basic idea of the post. It seems that it was just a post about a virtual game that has nothing to do with Blood Bowl. Funny, i thought it was a post to talk about Blood Bowl, and more precisely tactics and team development. Whatever could have given me that idea?

<b>TalkBloodBowl.com Forum Index -> Tactics & Team Development</b>

Oh yeah, that's it!

Seriously silverback_guerilla, if your intent was indeed to talk about gambling and not Blood Bowl, i think you should have said so from the start, and probably posted it in the off-topic forum as well. That would have avoided confusion.