Plasma Deck

Plasma Deck

Effect

Balance Chips and Mult when calculating score for played hand
X2 base Blind size

Unlock Requirement

Win a run with any deck on the Blue Stake difficulty or harder

The Plasma Deck is an unlockable deck that changes the way score is calculated in exchange for higher base Blind sizes. It is unlocked by winning a run with any deck on Blue Stake or higher.

Rather than multiplying Chips and Mult for scoring, the game averages out (balances) Chips and Mult before multiplying them, effectively calculating the score as ${\displaystyle {\left(\frac{\text{Chips}+\text{Multiplier}}{2}\right)}^2}$ rather than the normal ${\displaystyle \text{Chips}\times \text{Mult}}$.

For example, a Level 1 flush (10,8,7,6,4), would normally be calculated as

• 70 × 4 = 280

However, with the Plasma deck, the total Chips and total Mult are averaged together (or balanced) before they get multiplied.

1. 70 + 4 = 74
2. 74 / 2 = 37
3. 37 × 37 = 1,369

This is a significantly higher number and is offset by having Blind sizes twice as high when playing this deck. In fact, the hand score will almost always be higher after balancing (see #Mathematical Proofs).

Note that at higher Antes, the /2 becomes irrelevant, effectively making plasma deck a straight ^2 to your score.

Starting Contents[edit | edit source]

It contains the 52 cards of a normal deck: four suits, each with 13 cards (2 to 10, Jack, Queen, King and Ace).

Synergies[edit | edit source]

You want to aim for the highest raw number boosts to Chips and Mult. Since Chips start off at a higher number, most Jokers and Consumables boost Chips with a larger raw number than Mult (e.g. Bonus Card's +30 Chips vs Mult Card's +4 Mult). This is roughly balanced on other decks, but on the Plasma Deck, Chips and Mult equally contribute to the hand score, so using cards with large +Chips will result in a much higher score.

• 2,4,6,8,10 with Even Steven (Played cards with [[Card_Ranks|{{hl|orange|even}}]] rank give {{Mult|+4}} when scored <br> {{hl|gray|(10, 8, 6, 4, 2)}} Available from start. Common Additive Mult On Scored Even Steven.png) = 10 Chips and 10 Mult
• A,3,5,7,9 with Odd Todd (Played cards with [[Card_Ranks|{{hl|orange|odd}}]] rank give {{Chips|+31}} when scored <br> {{hl|gray|(A, 9, 7, 5, 3)}} Available from start. Common Chips On Scored Odd Todd.png) = 77.5 Chips and 77.5 Mult

In a normal deck, focusing on only XMult leads to a non-optimal distribution, which is fixed with the Plasma Deck and can result in much higher final scores with identical builds and the same hand.

• Normal Deck Scoring: 100 × 10,000 = 1,000,000
• Plasma Deck Scoring: 5,050 × 5,050 = 25,502,500
• This one is about 25.5x bigger!

Chip boosters:

• any Jokers that add large +Chips
• Bonus Card enhancement (+30 Chips)
• Foil edition (+50 Chips)
• Red seal will trigger the card twice, so you get twice the Chips
• higher rank cards (Ace card's +11 Chips vs Two card's +2 Chips)

However in later Antes, Chips only carry so far since they can only be additive in the base game (i.e. there are no XChips jokers in the base game). On the other hand, Mult can be multiplicative. While XMult is slow early on, with a high enough base Mult, this boost can be much greater than +Chips in the late game. In this example, one would need +4,000 Chips to match the power of adding a Polychrome:

• 1.5x Polychrome × 8 Mult = 12 Mult— the Polychrome effectively gives +4 Mult which balances to +2 Chips and +2 Mult
• 1.5x Polychrome × 8,000 Mult = 12,000 Mult—the Polychrome effectively gives +4,000 Mult which balances to +2,000 Chips and +2,000 Mult

This makes the Plasma Deck one of the best decks for Endless mode, since even though the score requirement per Ante is doubled, by focusing on the XMult, the score one achieves is almost squared from the score achieved in any other deck.

An Endless run example: 4 Polychrome Red Seal Glass 2s, Level 20 Four of a Kind, The Idol (Each played [[Card Ranks|{{hl|orange|[rank]}}]] of [[Card Suits|{{hl|orange|[suit]}}]] gives {{xmult|2}} when scored<br><small>Card changes every round</small> In one hand, earn at least 1,000,000 Chips. Uncommon Multiplicative Mult On Scored The Idol.png)/ Blueprint (Copies ability of [[Jokers|{{Hl|orange|Joker}}]] to the right Win 1 run. Rare Effect Blueprint.png)/ Hack (Retrigger each played {{hl|orange|2}}, {{hl|orange|3}}, {{hl|orange|4}}, or {{hl|orange|5}} Available from start. Uncommon Retrigger On Scored Hack.png)/ Brainstorm (Copies the ability of leftmost [[Jokers|{{hl|orange|Joker}}]] Discard a {{ph|Royal Flush}}. Rare Effect Brainstorm.png)/ Perkeo (Creates a [[Card Modifiers|{{hl|sblue|Negative}}]] copy of {{hl|orange|1}} random [[Consumables|{{hl|orange|consumable}}]] card in your possession at the end of the [[The Shop|{{hl|orange|shop}}]] Find this [[Jokers|Joker]] from the [[Spectral Cards|{{hl|sblue|Soul}}]] card. Legendary Effect N/A (Passive) Perkeo.png), and Observatory with 115 Negative Mars (Increases {{ph|Four of a Kind}} hand value by {{mult|+3}} and {{chips|+30}} Available from start. Planet Mars.png) cards

• Chips:
  • Each card gives 2 Chips × 4 triggers (one from card, one from Red Seal, one from Blueprint Hack, one from Hack) = 8 Chips
  • The resulting Chips is 630 (base) + (8 Chips × 4 cards) = 630 + 32 = 662 Chips
• Mult:
  • Each card gives an XMult of (2 Glass × 1.5 Polychrome × 2 Idol × 2 Brainstorm Idol)^4 retriggers = 12^4 = X20,736 Mult
  • The resulting Mult is 64 (base) × (20,736^4 cards) × (1.5^115 Mars (Increases {{ph|Four of a Kind}} hand value by {{mult|+3}} and {{chips|+30}} Available from start. Planet Mars.png) cards) = 64 × 184,884,258,895,036,416 × 178,030,655,708,718,648,266 = 2.1e39 Mult

On a regular deck, the resulting score is 662 Chips × 2.1e39 Mult = 1.4e42, which is enough to beat Ante 19.

But on the Plasma Deck, the resulting score is ((662 Chips + 2.1e39 Mult) / 2)² = (1.1e39)² = 1.1e78, which is enough to beat Ante 24.

This means, on the Plasma Deck, this build with the current setup has a headstart of 5 Antes.

Poker Hands[edit | edit source]

Playing many scoring cards is very efficient in this deck, example Two Pair:

A,A,10,10 = 62 Chips and 2 Mult, which becomes 32 Chips and 32 Mult = 1,024

Jokers[edit | edit source]

Stuntman ({{Chips|+250}},<br>{{hl|orange|-2}} hand size Earn at least 100 million (100,000,000) Chips in a single hand. Rare Chips Independent Stuntman.png) is very useful with the Plasma Deck, because it produces an incredible amount of Chips and doesn't need time to scale.

Wee Joker (This Joker gains {{Chips|+8}} when each played {{hl|orange|2}} is scored <br> {{Currently|{{chips|+0 }}}} Win a run in 18 or fewer rounds. Rare Chips Mixed Wee Joker.png) can also be incredibly useful with the Plasma Deck, however it requires a lot more time and focusing to reach an optimal level.

Any Endless build can benefit from the Plasma Deck; Perkeo (Creates a [[Card Modifiers|{{hl|sblue|Negative}}]] copy of {{hl|orange|1}} random [[Consumables|{{hl|orange|consumable}}]] card in your possession at the end of the [[The Shop|{{hl|orange|shop}}]] Find this [[Jokers|Joker]] from the [[Spectral Cards|{{hl|sblue|Soul}}]] card. Legendary Effect N/A (Passive) Perkeo.png) can be used for copying Planet cards for the Observatory voucher, where the amount of Planets needed is less than usual due to each Planet boosting the score by almost the square of the amount as on any other deck. Sixth Sense (If {{hl|orange|first hand}} of round is a single {{hl|orange|6}}, destroy it and create a [[Spectral Cards|{{hl|sblue|Spectral}}]] card <br> {{room}} Available from start. Uncommon Effect N/A (Passive) Sixth_Sense.png) and Séance (If [[Poker Hands|{{hl|orange|poker hand}}]] is a {{ph|Straight Flush}}, create a random [[Spectral_Cards|{{hl|sblue|Spectral}}]] card <br> {{room}} Available from start. Uncommon Effect Independent Séance.png) can generate a Cryptid (Create {{hl|orange|2}} copies of {{hl|orange|1}} selected card in your hand Available from start. Spectral Cryptid.png) in the consumable area, which can also be copied by Perkeo (Creates a [[Card Modifiers|{{hl|sblue|Negative}}]] copy of {{hl|orange|1}} random [[Consumables|{{hl|orange|consumable}}]] card in your possession at the end of the [[The Shop|{{hl|orange|shop}}]] Find this [[Jokers|Joker]] from the [[Spectral Cards|{{hl|sblue|Soul}}]] card. Legendary Effect N/A (Passive) Perkeo.png) (for Baron (Each {{hl|orange|King}} held in hand gives {{xmult|1.5}} Available from start. Rare Multiplicative Mult On Held Baron.png)/ Mime (Retrigger all card {{hl|orange|held in hand}} abilities Available from start. Uncommon Retrigger On Held Mime.png) builds) — the amount of Cryptid (Create {{hl|orange|2}} copies of {{hl|orange|1}} selected card in your hand Available from start. Spectral Cryptid.png)s needed is also less than usual, since each Cryptid (Create {{hl|orange|2}} copies of {{hl|orange|1}} selected card in your hand Available from start. Spectral Cryptid.png) boosts the score by almost the square of the amount as on any other deck.

Mathematical Proofs[edit | edit source]

Proof that balancing (almost) always increases a hand's score[edit | edit source]

This is a case of the AM–GM inequality. Let Chips be C and Mult be M. Their difference is defined as D = C − M. Expanding D², we get D² = C² + M² − 2CM. The normal hand score, before balancing, is given as CM.

$${\displaystyle \begin{array}{lcl}\text{Balanced Hand Score}& =& {\left(\frac{C+M}{2}\right)}^2\\ & =& \frac{C^2+M^2+2CM}{4}\\ & =& \frac{C^2+M^2-2CM+4CM}{4}\\ & =& \frac{C^2+M^2-2CM}{4}+\frac{4CM}{4}\\ & =& \frac{D^2}{4}+CM\\ & =& \frac{{(C-M)}^2}{4}+\text{Normal Hand Score}\end{array}}$$

Because (C − M)² is always greater than or equal to zero, the balanced hand score will always be greater than or equal to the normal hand score. They will only be equal if C equals M, indicating the normal hand score was already balanced. This inequality is expressed as,

$${\displaystyle {\left(\frac{C+M}{2}\right)}^2\ge CM}$$

which is a form of the AM-GM inequality. $◼$

However, this assumes no rounding. In reality, balancing rounds half-down, which can in some cases actually reduce the final score. For example, if Chips and Mult differ by exactly 1:

Before balancing, score = CM = n(n+1) = n² + n

After balancing, score = floor($\frac{2n+1}{2}$)²

= n²

which is less than n² + n.

Plasma Deck requires a 5.8x ratio between Chips and Mult to be as effective as other decks[edit | edit source]

Due to Plasma Deck's doubled Blind size, some hands are less effective at beating a large Blind when played on Plasma Deck. A hand's effectiveness can be measured as its score divided by the Blind size—like the Blind has an HP bar and a hand reduces it by a percentage. At worst, a hand can be twice as ineffective on Plasma Deck if its Chips and Mult are exactly equal, as balancing doesn't increase the score, yet the Blind size is doubled.

Plasma Deck thus encourages the player to build towards heavily scaling either Chips or Mult—typically Chips in the early game as it's easier to get a decent number of Chips quickly, then pivoting to Mult later as it scales faster in the long run with XMult effects. Otherwise, if the player had built towards having relatively balanced Chips and Mult, balancing again would not provide enough of a buff to overcome the doubled Blind size debuff, and the hand ends up being less effective, especially at larger blinds. Specifically, a hand's Mult has to be around 5.8x its Chips, or its Chips around 5.8x its Mult, for the hand to be as effective on Plasma Deck as on a normal-scoring deck. What follows is a proof:

Let Chips be C and Mult be M. The normal hand score is given as CM, while the balanced hand score is given as${\left(\frac{C+M}{2}\right)}^2$. The effectiveness of a given hand is measured as its score divided by the Blind size S. On a normal-scoring deck, this is measured as $\frac{CM}{S}$; on Plasma Deck, it is measured as $\frac{(C+M{)}^2}{8S}$ where the doubled Blind size 2S is accounted for. To find the Chips–Mult ratio C/M where a hand becomes equally effective on both decks, set the two measures equal:

$${\displaystyle \begin{array}{rcl}\frac{CM}{S}& =& \frac{(C+M{)}^2}{8S}\\ 8CM& =& (C+M{)}^2\\ 8CM& =& C^2+M^2+2CM\\ 0& =& C^2+M^2-6CM\end{array}}$$

Solve for C using the quadratic formula, treating M as a constant:

$${\displaystyle \begin{array}{rcl}C& =& \frac{6M\pm \sqrt{(6M{)}^2-4M^2}}{2}\\ & =& \frac{6M\pm \sqrt{36M^2-4M^2}}{2}\\ & =& \frac{6M\pm \sqrt{32M^2}}{2}\\ & =& \frac{6M\pm 4\sqrt{2}M}{2}\\ & =& 3M\pm 2\sqrt{2}M\end{array}}$$

The two solutions are approximately:

$${\displaystyle C\approx 5.828M\text{ and }C\approx 0.172M}$$

These solutions are reciprocals of each other, which means either C/M ≈ 5.828 or M/C ≈ 5.828. $◼$

In other languages[edit | edit source]