Variable Scoring Explained

The rule, in two sentences

At the end of a round, every losing player draws one card off the top of the deck. That card multiplies whatever the round was worth to them, so two people can lose the same round and owe completely different amounts.

An ace counts as 1. The number cards count as their face value. The ten, jack, queen and king all count as 10. That's the entire rule, and the rest of this page is what it adds up to.

The math

The expected multiplier is 85/13, which is 6.54x. Here's where every part of it comes from:

Card	Multiplier	Cards	Share of deck	Contribution
A	1x	4	7.7%	0.08
2	2x	4	7.7%	0.15
3	3x	4	7.7%	0.23
4	4x	4	7.7%	0.31
5	5x	4	7.7%	0.38
6	6x	4	7.7%	0.46
7	7x	4	7.7%	0.54
8	8x	4	7.7%	0.62
9	9x	4	7.7%	0.69
10, J, Q, K	10x	16	30.8%	3.08
Total		52	100%	6.54

Look at the bottom row before the total. Those sixteen cards contribute 3.08 of the 6.54, which is 47% of the entire expected multiplier sitting in one line of the table. That's what happens when four separate ranks all resolve to the same maximum.

Weighting the deck changes nothing

The instinct when you see a table like that's to say the simple average over the thirteen ranks must be wrong, because the tens and face cards stack up and should pull it higher. So weight it by how many cards are actually in the deck.

Do that and you get 340 divided by 52, which reduces to 85/13. The same number, exactly.

It comes out identical because every rank has precisely four cards in a standard deck, so the weights are uniform and cancel. Weighting only matters when some outcomes are more common than others, and here none of them are. The four 10x ranks aren't four times as likely as the ace, they're four separate ranks that happen to pay the same.

One honest caveat: this is the full-deck expectation. In an actual hand the deck has already been dealt from, so the live number drifts a little depending on what has come out. Over a night it lands close.

What the distribution looks like

The average is one number and it hides the shape. Three more:

• Median: 7x. Half of every draw ever made comes in at 7x or better.
• Most common outcome: 10x, at 16 of 52 cards. Nearly a third of the deck is the maximum.
• 69.2% of the deck is 5x or more. Only 12 cards out of 52 come in at 3x or under.

So the typical round isn't a mild adjustment to the score. It's a 7x round, and roughly one in three is the biggest one available.

Setting a number you actually want

Here's where 6.54x earns its keep. People set the per point amount thinking that's what a round costs. It isn't. With variable scoring on, the number you set is what a round costs before the multiplier, and the multiplier averages 6.54.

So divide by 6.54 rather than guessing. If you want a lost round to average around $50, set roughly $7.50 per point. For $25, set about $3.80. Set $5 without doing the arithmetic and your average lost round is $32.69, with $50 possible any time somebody peels a face card.

You set	Average lost round	Biggest possible round
$1	$6.54	$10
$5	$32.69	$50
$10	$65.38	$100
$25	$163.46	$250

For a whole night, add one more term: how often you're the one drawing. With four players you lose about three rounds in four, so twenty rounds at $5 comes to roughly $490 of expected downside across the night. Work it backwards and a $100 night over twenty rounds of four-handed lands at about a dollar a point.

Single and Series behave differently

In Single, the draw happens at the end of every round. Lose three rounds, draw three cards.

In Series, it fires exactly once, when somebody actually wins the series. Nothing happens on the rounds along the way, so a series that looked like a quiet grind can resolve into something enormous on the final card, and everyone can see it coming the whole time.

The squeeze

The card arrives face down and you turn it over yourself, slowly, the way you would peel a hole card. Everybody at the table watches. In an online room the other players see the back of your card and a note that they're waiting on you, and it flips on their screens the moment it flips on yours.

One detail took a rebuild to get right. The running total at the bottom of the screen doesn't move until every loser has revealed. In an early version the app scored the round first, so you could glance at the ledger and work out your card before you turned it over. The number was correct and the moment was ruined.

When we turn it on

I play with it on almost always. With flat scoring, whoever wins the most rounds grinds out a small edge and everybody goes home roughly level, and I would rather one round be able to swing the whole night.

Plenty of people feel the other way and they aren't wrong about it. If your table wants the score to reflect who actually played better across an evening, variable scoring cheerfully wrecks that, which is exactly why it's a toggle and not a rule.

When somebody at the table is learning the games we usually leave it off for the first night, because there's enough going on already.

FAQ

What is the average multiplier?

6.54x, or exactly 85/13. Ace counts as 1, the number cards count as their face value, and 10, jack, queen and king all count as 10. Add the thirteen ranks and you get 85, divided by 13 ranks is 6.538.

Does weighting by card count change it?

No, and that surprises most people. Every rank has exactly four cards in the deck, so the weights are uniform and cancel out. The card-weighted average over 52 cards is 340/52, which reduces to the same 85/13. You only need to weight when some outcomes are more common than others, and here none of them are.

What are the odds of drawing 10x?

16 cards out of 52, so 30.8%. Nearly a third of the deck is the maximum multiplier, because the ten and all three face cards land on the same value. Those 16 cards contribute 3.08 of the 6.54 expected multiplier on their own, which is almost half.

What is the median multiplier?

7x. Half of all draws come in at 7x or higher. 36 of the 52 cards, or 69.2%, are 5x or better, and only 12 cards are 3x or under.

Does it work with Series mode?

Yes, and the timing changes. In Single mode the draw happens at the end of every round. In Series mode it only fires once, when somebody wins the series, so the whole series gets multiplied at the finish instead of round by round.

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