"Unique Blackjack Combinations By Hand Total And Number Of Cards"

So im always prodding at chatgpt. Seeing how it improves, if it ever will.

Today i wanted to know Unique Blackjack Combinations By Hand Total And Number Of Cards based on 6 and 8 deck amounts.

This is my prompt and its repsonses

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in a six - eight deck blackjack game list all of the combinations of cards that will make 21 up to a 10 card hand

since my query was essentially garbage to the ai it took some talking to get to a more narrow understanding and it eventually got what i wanted... i think

Quote:

Here's the updated chart reflecting realistic card limits from 6 decks (e.g., only 24 Aces and 96 Tens available). The counts are now based on valid combinations that could physically be dealt within that constraint. Let me know if you want the same for 8 decks or a specific total exported.
6 deck

8 deck

What im seeing is that, its way easier to get 21 the higher number of cards in 6 and 8 decks

does 98 combinations of 6 card 21s sound right? This seems like a hallucination to me because the 8 and 6 deck amounts are the same in each picture given

chatgpt insists...

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something seems off about your 6 and 8 deck charts in the sense that 98 combinations of 6 card hands that equal 21 does not seem possible for both

Quote:

ChatGPT said:
You're right to question it — it does seem surprising that both the 6-deck and 8-deck environments yield exactly 98 unique 6-card combinations that total 21.

But here's why it's actually possible:

The limit on card counts (e.g., 24 of each value in 6 decks vs 32 in 8 decks) only begins to matter when a combination requires more instances of a value than exist in the shoe.

A 6-card hand has relatively low demand on card count variety. In nearly all valid combinations of 6 cards totaling 21, no single card value is used more than 4 or 5 times — well below both decks' limits.

So in this case:

All 98 valid 6-card combinations that sum to 21 can be formed using only what's available in a 6-deck shoe.

Increasing to 8 decks doesn’t introduce new combinations — it just provides more ways to realize them, which we are not counting (we count only unique value sets, not permutations or frequency of appearance).

If you'd like, I can list the 98 combinations for inspection — or highlight which hand sizes start to diverge between deck sizes.

Your question is too complicated. Simplify it.
What is the probability of a 3-card 21 hand?
What is the probability of a 4-card 21 hand?
What is the probability of a 5 or more card 21 hand?

are your combinations sequence-specific or sequence-independent? (other than the proviso that hands making a soft 17-20 are no further hit.)

Are
2-3-7-A-8
and
3-2-7-A-8

counted as two combinations? or the same combination?