Maths question on three jokers

[MadBone12]

I have looked at this joker hand for some time and still can't understand the best place to use the Blueprint card. I was hoping someone could help.

https://steamcommunity.com/sharedfiles/filedetails/?id=3548738357

Now, I know that this is actually not a very good joker set. I need more +mult - this is more of a question about understanding the general maths for the first three cards on the left, next time I have all three.

My specific question: let's assume that most of my face cards have +mult or are glass, and that I have also levelled up whatever hand I am going to play. If I want to play a hand with face cards, then what is the best way to use the blueprint? Do I use it before the Hanging Chad, where it is now (and make sure that my first card is a face card), or before the next card to the right which gives XMult for the first face card?

[Ronald Brain]

Let's just assume that you play a level 1 Flush with a +4 Mult King:

Base mult: 4
BP+Hanging Chad then Photograph: 8x2, then +4 x2 four times = 376 mult
Hanging Chad then BP + Photograph: 8x2x2, then +4 x2x2 three times = 592 mult

(I may be off a bit, this is just going in my head, but it should be similar)

The basic rule is that you should keep the number of multiplier and retrigger as balanced as possible.

[SadPlatty©]

After some quick-and-dirty math, it would appear that you would want BP to copy the half joker, while Chad does it's thing on the first card (which would obv want to be a face).

I used high card base level and ranked 2x coming up with the following scenarios :
- BP + Chad + Half on Lvl1
-- (10+10+10+10+10)*(2*2*2*2*2) = (60)*(64) = 3840
- Chad + BP + Half on Lvl1
-- (10+10+10)*(2*2*2*2*2*2) = (30)*(128) = 3840

So the level 1 hand is the same funny enough. But then you rank it up twice to get :
- BP + Chad + Half on Lvl3
-- (25+25+25+25+25)*(4*2*2*2*2*2) = (125)*(128) = 16000
- Chad + BP + Half on Lvl3
-- (25+25+25)*(4*2*2*2*2*2*2) = (75)*(256) = 19200

So it's not exactly going to break the bank if you forgot to move it on a play of non-enhanced cards or whatever, but the higher you scale the played hand, the more it will matter.

Per your last paragraph though - the Glass and Mult cards being played can matter as they would play best with Chad (even the glass x2 being before the other Jokers would make the "125" vs "75" a situation of "+128mult" vs "+4mult" against "+32mult" vs "+4mult" - resulting in the last values being "4096mult" vs "2048mult".


TL:DR - BP the Half for base playing card hands, otherwise flip it to BP Chad on mult enhanced cards to maximize their input (as chips won't matter as much as you get to later blinds). Seems the right way to go anyway I think.

[Barrows]

I think this is a great joker set.
You are copying Chad so the first card scores 5 times.
5 = 1+2(Chad)+2(Blueprint)
with Photo:
[base mult] x (2*2*2*2*2) = [base mult] x (2^5) = [base mult] x (32)

If you are copying Photo:
[base mult] x (2*2)*(2*2)*(2*2) = [base mult] x (4^3) = [base mult]*(64)
The first face card scores 3 times but gives you x4 per score because you "have" two Photographs.

If the first card is a glass card but not a face card then you have the first case, copying the Chad = x32 mult

If you have a glass face card then copying Chad is better:
[base mult] x (4*4*4*4*4) = [base mult] x (4^5) = [base mult] x (1024)

With copying photo and the glass card:
[base mult] x (8*8*8) = [base mult] x (8^3) = [base mult] x (512)

[MadBone12]

Thanks so much for all of the responses. I read them each a couple of times to get the gist and I am seeing a pattern. Generally, BP is likely to do better before the Photograph but there are specific scenarios in which it's better to use it before the Hanging Chad, such as a first glass face card. The level of the hand is also important so I will need to factor that in. Obviously, the first card needs to be a face card for BP to get any value before the Photograph.

Thanks again for the help.

[malogoss]

The following is just a slightly different way to present the good info you already got from other replies. It's very similar to what @Barrows already said. Honestly, my post might not be worth reading, idk. Up to you.
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Rule of thumbs, with nothing fancy going on, you want to copy Photograph first. Why?

Not accounting for Blueprint, you are getting your first card to trigger 1 (default) + 2 times (Chad), giving you x2 to mult each time because of Photograph.

Now we consider the Blueprint. By copying the Photograph, you "double" the amount of "x2" you get from that first card. If you copy the Chad instead, you are not quite doubling the amount of "x2" you are getting. You go from 1 + 2 to 1 + 2 + 2 triggers. Or from 3 to 5. That is only a 67% increase of the amount of "x2" effects you get. When you were copying Photograph, it was a 100% increase.
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When you have fancy things going on, rules of thumbs often fail. Including the one above.

If your first card is a glass card, without Blueprint, you are getting 3 triggers, each giving you two "x2" effects (one from glass, one from Photograph).

Add another "x2" effect by copying the Photograph, it effectively adds 50% to the amount of x2 effects you were getting. From 2 to now 3 per trigger, with the same amount of triggers at the end.

Copy the Chad instead and then, like previously, you are adding 67% to the amount of "x2" effects you are getting. 67% > 50%, so copying the Chad is better.
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In general, it can easily be broken down to how many times you are getting an effect and what is that effect, So you count how many times you get a "x2", biggest amount wins.

If you throw in a holographic card, a +4 mult card, or a card that is worth 110 chips because of a Hiker you had, then each trigger is worth more than with a simple plain card. That will always make copying the trigger joker better than it was by default, but is it really enough to not copy the Xmult joker? No rule of thumbs in this case.

On the opposite, if your first card is a red seal card with no other bonus, that tends to favor copying the Xmult joker (photograph) rather than the trigger joker. Because from
1 + 1 (red seal) + 2 (Chad)
to
1 + 1 (red seal) + 2 (Chad) + 2 (copying the Chad) triggers,
it's only a 50% improvement, it's not +67% anymore.

[RazzberryMocha]

A simple (or at least the simplest) way to think of it is with the equation (2^x)^y, with x being your Xmult triggers and y being your triggers. Our goal is to make x and y as balanced as possible. Also note this works with other effects like triboulet/sock or baron/mime.
In your example you have one photograph and one hanging chad. x = 2 because of your one photograph, and y = 3 because of your chad plus the initial trigger which results in (2^2)^3. The answer is to move blueprint onto photo for (2^4)^3, as with additional mult sources you multiply the x value.

[MadBone12]

Thanks for the additional responses. I did read them (after a few days break from the forums).

I've gotten a similar set of jokers since then and broke a few personal records for single hands and antes, using glass face cards, BP, Hanging Chad and Photograph. Thanks for the advice.