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Subject: Opening hand analysis rss

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Alex Arkhipov
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How many coins can you score on your first two hands? Here's a needlessly in-depth analysis.

It depends on how the five initial consonant cards LNRST split in number between the two five-card hands (3/2, 4/1, or 5/0), and what the common card is. A vowel common card is almost always usable, Dyslexia is never usable, and Spacebar requires 2+ wilds in hand. Using the common card both times gives 7¢ total, unless one hand is too short on wilds to use all its letters.


+-------+-------+-------+-------+
| | Vowel | Dys | Space |
+-------+-------+-------+-------+
| 3/2 | 4¢/3¢ | 3¢/2¢ | 4¢/3¢ |
| 4/1 | 5¢/2¢*| 4¢/1¢ | 4¢/2¢ |
| 5/0 | 5¢/1¢ | 0¢/0¢ | 0¢/0¢ |
+-------+-------+-------+-------+
*Except LNR?T with common O gives 4¢/2¢


Note that the specific letters rarely matter, just their distribution. (This uses words in OSPD5, the official Scrabble dictionary. Paperback doesn't specify what decides which words are legal.)

Let's break down the cases:

2 or more wilds in hand:
It's easy to use all your letters and a common vowel or space. For Spacebar, make a two-letter like Lo, No, oR, So, To with wild as O, plus a three letter word.

1 wild in hand: You can still usually get the most out of your hand. Find your hand in the left column of the table and the common card on the top row.

+---------+------------+------------+-------------+------------+-------------+
| | A | E | I | O | Dys / Space |
+---------+------------+------------+-------------+------------+-------------+
| ?NRST | RANTS | RENTS | STRaIN | SNORT | RaNTS |
| L?RST | TRAiLS | LuSTER | TRaILS | TROLlS | TiRLS* |
| LN?ST | SLANT | iNLETS | INLeTS | STOLeN | SLaNT |
| LNR?T | ReNTAL | RENTaL | NITRiL* | TONeR (-L) | LaRNT* |
| LNRS? | SNARL | LEaRNS | LINeRS | LONeRS | SNaRL |
+---------+------------+------------+-------------+------------+-------------+
| LNRST | RANTS (-L) | RENTS (-L) | LINTS* (-R) | SNORT (-L) | (-LNRST) |
+---------+------------+------------+-------------+------------+-------------+


(Words marked with * are obscure words in the OSPD5 Scrabble dictionary that your playgroup might object to.)

With a vowel common, you can get the maximum 5¢. The exception is that LNR?T with common O can't all be used together, wasting a cent. Spacebar can't be used with only a single vowel; none of the Scrabble consonant-only words can be made from LNRST. You can still use all 4 consonants in hand for 4¢.

No wilds in hand: With LNRST in hand, any common vowel still allows a 5-letter word for 5¢ (see table above). Otherwise, you can't make anything, so you're dead in the water, with your five-wild other hand useless too.


Let's look at probabilities.

Chance: 4/6 1/6 1/6
+-------+-------+-------+-------+
| | Vowel | Dys | Space |
Chance: +-------+-------+-------+-------+
100/126 | 3/2 | 4¢/3¢ | 3¢/2¢ | 4¢/3¢ |
25/126 | 4/1 | 5¢/2¢*| 4¢/1¢ | 4¢/2¢ |
1/126 | 5/0 | 5¢/1¢ | 0¢/0¢ | 0¢/0¢ |
+-------+-------+-------+-------+
*Except LNR?T with common O gives 4¢/2¢
1 in 20 chance within this category


The 3/2 split happens about 80% of the time, giving an easy 4¢/3¢ (3¢/2¢ with Dyslexia). The 0¢/0¢ ruin has about 0.6% chance. Overall, there's an about 5% chance of not getting the maximum 7¢ (5¢ if Dyslexia), the majority due to Spacebar with a single wild.


With the "Discard hand for a cube" optional rule, you can turn a wasted 0¢ or 1¢ turn into a cube for +1¢ later, which takes some of the sting out of an unlucky opening. When this happens on the first hand, it can boost your opening. For example, 1¢/5¢ can become --/6¢.
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Tim Fowers
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Excellent analysis!

I've been thinking about some new starting decks for an expansion. You have any ideas of what would be good alternate deck composition?

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Alex Arkhipov
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I think this depends on what you're hoping for the first two turns to mean.
If you want the opening to just give a 4/3 split most of the time with minimal chance of screwage, the current deck is great for that. Rarer starting letters would be more skill-testing and make the starting plays more variable and meaningful, though some might find it too stressful to fall behind already on turn 1 and 2. Rarer letters could be diluted by having 4 letters and 6 wilds, or even some starting vowels.
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