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Subject: Playing the odds rss

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P.D. Magnus
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PROPERTIES

Obviously, it's better to have a rank 9 property than a rank 6 property. But is it better than a rank 6 and a rank 3 property together?

In Magnate, a property does two obvious things for you: It contributes to your control of the district (at the end of the game) and generates income (over the course of the game).

In terms of district control, a 6 and a 3 count for the same as a 9.

Income is a bit trickier. The resource roll each turn is the greater of two ten-sided dice. Here's the chances of each payoff:
19% Crown
17% 9
15% 8
13% 7
11% 6
9% 5
7% 4
5% 3
3% 2
1% Ace
So a 6 or 3 will hit 16% (=11+5) of the time, which is slightly worse than the 9's 17% - but only slightly.

A third thing to consider, however, is you can only play one card per turn. The 6 and the 3 take two turns to play, but the 9 only takes one turn - you can use the extra turn to develop something else or to sell a card.

This issue of timing can make a big difference in the final turns of the game. It is no help to have lots of low ranked cards if you don't have time enough to develop them all. So higher ranked cards can make a big difference at the end of the game. Of course, the 9 may be too expensive to develop in the last few turns. A 6 might be the sweet spot combination of affordable and potent. It varies from game to game.

The upshot is that a 9 is better than a combination of smaller cards, but not by as much as your might think. I have certainly played games in which one player draws two or even all three 9s but loses.

TAXES

As long as I'm calculating odds, what about taxation?

On each player's turn, there is a 19% chance of taxation.

What matters, though is the chance that taxation will strike after your turn ends but before you can spend resources. Your opponent will roll the dice and then you will, and the chance of taxation occurring at least once in those two rolls is 34%.

The longer you keep surplus resources, the greater the chance becomes. After five of your turns, the chance of taxation at least once rises to 88%.

Perhaps you only have a surplus in one resource. Since taxation effects a single random resource each time it occurs, how safe should you feel? The chance that taxes will sap your favourite resource before your next turn is about 6%. In five of your turns, the chance rises to nearly 28%.
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Jeremiah Lee
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Thanks, this is excellent to have. I've been considering what the odds were, but never went through the process of actually calculating them.
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Jack Neal
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This reinforces what my 7-year-old and I had noticed - resources take /forever/ to pick up. We were considering coming up with a variant on the game to loosen things up a little bit, but we didn't come up with anything and got lost on some maze playing game of yours. :-)

Excellent work!
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P.D. Magnus
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Raiderjakk wrote:
This reinforces what my 7-year-old and I had noticed - resources take /forever/ to pick up. We were considering coming up with a variant on the game to loosen things up a little bit, but we didn't come up with anything and got lost on some maze playing game of yours.


Two things to note in standard Magnate: If you aren't developing anything, you have to sell a card on your turn - which will give you some income. Also, you can buy a deed for just two resource tokens - it can make some income while you save up to complete development.

If you still think that the economy is too tight, here's a variant that Jorge Arroyo suggested: If the higher roll of the 2d10 doesn't generate resources for either player, use the lower roll instead for that turn. For example: You roll a 9 and a 3 when there are no 9s in play; any 3s in play provide resources for that turn.

The variant makes lower-ranked cards much more valuable early in the game, before anything else is on the table. It also may give you a chance to screw your opponent; not only will your deed on a 9 be good for you, it will also stop their lower cards from getting income when a 9 is rolled. Be warned, though, that the variant is almost entirely untested.
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Jack Neal
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Quote:
If you still think that the economy is too tight, here's a variant that Jorge Arroyo suggested: If the higher roll of the 2d10 doesn't generate resources for either player, use the lower roll instead for that turn.


That might be worth trying out... It had crossed my mind to do that, but I wasn't sure what it would do.

Off topic, but the Crowns cards look like a great addition! Hopefully a publisher picks them up for you.
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Jeremiah Lee
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I haven't really felt like the resources haven't been enough. I mean, I've had games where there have been low resources, but not usually. Overall it's seemed to usually be a difficult choice between deeding the high ranks, or fully paying for a lower rank, and I think that's the goal.
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