Can somebody figure out the value of this offer? (probability q)

If they have computers monitoring play, it’s only to detect evidence of counting (which also slightly distorts optimal play, depending on the count). Non-counting basic strategy, they’re cool with (they’ll even give you a quick-reference sheet for it).

And with a CSM they don’t care about card counting at all, as it’s impossible.

Ah, I glossed over that it was a continuous-shuffle machine. I didn’t realize those were in significant usage by casinos-- I thought they depressed customer count too much.

EDIT: That is to say, quantity of customers. They’re supposed to depress people counting cards.

I respectfully disagree - since Blackjack is a negative EV proposition (especially with a CSM), you want to minimise the time you spend at the table to maximise the EV of the overall proposition. Or at least, certainly where the basic strategy choice is a toss-up anyway. And probably where it is only slightly more one way than the other.

Incidentally, I think the game idea is pretty clever on the casino’s part - most people, unlike the OP, are going to be drawn into it, thinking that once they have 3 or 4 symbols ticked off they are nearly there, encouraging them to keep playing. Perhaps forgetting that of course the closer you get to the goal, the longer your odds on each spin being successful. Requiring just 2 symbols to get the prize, for example, the chances are 6/121 (just under 5%) if you only have 2 spins to do it, but it ‘feels’ like you are only 2 spins away from success. So example #73 of why feelings are a terrible guide to estimating probabilities.

ETA: I await any further updates from the OP with interest!

Since you ask, I got down to [6,1], but couldn’t get that last one in the 6 remaining spins, nothing for me.

It’s not impossible, it’s just a lot less useful. You can count the cards in the current hand, and if you’re playing third base at a full table, you’ll get to see a fair number of cards before you play. But depending on the number of decks in play, that will still probably be a small fraction of the cards.

I’ve never done it and never would, but as I understand it the benefit to card counting is the ability to change your stake, not your strategy. Only on rare occasions with deep penetration into a shoe does actually changing strategy have any benefit. You are not going to get that with a CSM

Aside: I just realized how clever the OP’s avatar is. I had dismissed it at first as just “oh, he likes to play cards”, consistent with the thread topic. But then I looked again at the username.

A good card counter will both vary his bet and vary his strategy. For example, here is a system with a chart showing 18 cases where you’d vary your strategy based on the count: Introduction to the High-Low Card Counting Strategy - Wizard of Odds. I’ve done a lot of card counting but not at a very advanced level and I usually mostly just vary my bet, and use only the most important strategy changes. But I don’t count at CSM tables; it’s too much work for not enough benefit. If I did count at a CSM table I would pretty much have to vary the strategy to make it worthwhile. Although there are some opportunities to modify your bet after play has occurred, when you double or split.

Commiserations to the OP - I make it you were odds-on favourite with six spins needed to get the last symbol, about a 70% chance of success (calculated as 1 - (9/11)^6, but perhaps I have made an error).