Goblin Game for Nick

Hi Nick!

I did a quick and dirty analysis of Goblin Game for you. In order to do so I had to make some assumptions.

1) Neither player knows what the other is likely to bid
2) You both are at 20 to start
3) Your bidding is limited by how many things you can hold in your hand covertly, I assumed 10.

I know #2 isn't super likely, given the converted cost of 7, but I had to start somewhere, and we can discuss how it changes with different starting totals without redoing all of the math.

So here's a chart of what happens when you bid any given number, and your opponent bids randomly between 1 and 10. While their bid won't be random, of course, it might as well be as your knowledge of it is none.

Your Bid	Average Loss	Opp Avg Loss	Diff
1	10.9	6.4	-4.5
2	10.1	7.4	-2.7
3	10	8.2	-1.8
4	9.4	8.9	-0.5
5	9.5	9.6	0.1
6	9.2	10.3	1.1
7	9.4	10.9	1.5
8	9.4	11.5	2.1
9	9.7	12	2.3
10	10	12.5	2.5

So to get the most bang for your buck, you're going to want to bid high. Of course, in reality you can also intimate from game clues and context clues and super secret Rounders-level tell reading about what your opponent will bid, and try to bid just above them.

Here's the same chart in graph form, because graphs!

Now, to address the reality of the situation:

If your life totals are unequal, things get trickier. A player with less total life risks less by wagering low (because the penalty of losing half is less in absolute terms), but exposes themselves to greater danger because of the relative danger of getting dead from your opponents' tricks. On the other hand, if you have a lower life total relative to your opponent, you can be locked into the losing bid by an opponent who bids higher than your overall life total.

In general, as your life decreases, you should bid lower. For example, a player with 5 life can bid 1 with more impunity than a player at 20. Usually, bidding 1 is a bad idea, but as your life score gets lower, it becomes less of a bad idea.

One final note, the minimum you (and your opponent) can lose is 2 life. If your opponent is at 2 and you're at more than 2, just bid 1 and you win!

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