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The most pointless rule in the history of blackjack

One of the online casinos I have been bonus-whoring at has a blackjack game with a "7-card Charlie" rule.  If you manage to draw seven cards without busting, your hand is automatically a winner against anything except a dealer blackjack.

I know every little is meant to help, but according to The Wizard of Odds, this rule is virtually worthless.  It reduces the house edge by just 0.01%.

If you think about it, even with six decks of cards there’s only a very small number of ways you can be dealt a seven card hand like this if you’re playing basic strategy.

You could do it just with 2s and 3s, but it’s going to help if there’s at least a couple of aces in there, and if your first two cards are aces, you always split them so any combinations beginning with AA are never going to go to seven cards.

Often you’ll split pairs of 2s and 3s too, and you’ll double down for one more card on your A2 and A3 against a dealer 5 or 6.

If you start with just one ace, you’ll stop drawing cards on a soft 17 or 18 against most of the dealer’s up cards, and you’ll always stand on a soft 19-21.  So to get a seven card hand, you have to skip past that "standing zone" quite specifically (for example: A, 2, A, 2, 6) and then carry on taking cards once you get to 12 or higher.

Because you’re always going to stand when you get past hard 17, the only way to get for a 7-card Charlie is to pull a six-card hand totalling 16 or lower, and then hit for one final card that doesn’t bust you.

And once you’ve got that close, a fair amount of the time you’ll hit up to 20 or 21 anyway, which means the value of the Charlie is really very small indeed.  A seven-card 20 or 21 would beat most dealer hands regardless of the special rule.

If the rule was for a 6-card Charlie, it would (according to The Wiz) improve the game by 0.16% – still tiny, but just about significant enough to adopt some strategy changes to take advantage of the rule.

If the house offers a five-card Charlie, they give the player back a theoretical 1.46%, and in most games this rule alone could push the game into a positive expectation.  Which explains why I’ve never seen it offered in any casino, live or online.

So then, what is the point of a ten-card Charlie rule?  This is a variation of the rules in just onegame at an online casino I like very much (they have a $100 bonus that can be easily cleared in a few hours and don’t ask for ID to withdraw!).  The help pages say:

It is theoretically possible for the player to draw 10 cards without going bust.

Well, yes it is, but if you are following basic strategy, I have only found of a tiny number of ways that this will ever happen.  As you might expect, it involves a whole bunch of aces, and there’s no way it’s ever possible in a single-deck game.

If the dealer upcard is a 2 or 3, we have to stand on a hard 13 or higher, or a soft 17 or higher.  There is no possible 10-card hand that can be made against these cards.  In fact six cards is the most possible if you start with an ace: A, 2, A, A, A, A = 17.  Begin with a 6-card 12 (2, 2, 2, 2, 2, 2) and hit once more and you can make a 7-card Charlie.

When the dealer shows a 4, 5 or 6, we double down any soft total if the rules allow it.  If it’s not allowed we have to stand on a soft 17 as well as a hard 12, and this still only leaves us a 7-card hand at best: A, 2, A, A, A, 6, A = 13.

If the dealer upcard is 7 or 8, we can hit soft 17 and all hard totals up to 16.  Now we’re in business:

- First, we have to be dealt precisely an A, 2 (cards: 2, total: 3).
- Next we have to be dealt 3 more aces, or two aces and a 2 (cards: 5, total: 6 or 7).
[Or four aces is also possible here for a 6-card soft 17]
- To avoid standing on soft 18-21, the next card has to be a 5 or 6, whichever makes the total up to 12 (cards: 6 or 7, total: 12)
- We then need either A, A, A or A, A, 2 (cards 9, total: 15/16)
- Finally we can pull one more card and hope to not bust (cards: 10, total 16-21)

We could also start with a six-card 12 or 13 (six 2s, or five 2s and a 3) to avoiding all the soft totals that would require us to stand, and then draw three aces and one final small card.

Given the very small number of possibilities, it’s quite possible to calculate out the actual probability of getting dealt a winning 10-card Charlie.  I’m going to lose marks for not showing my working, but I get an answer in the region of trillions to one.  I don’t think the precise number matters particularly when it’s so extremely rare…

If the dealer upcard is 9, T or A we actually have a few more options than for a 7 or 8, because we have to hit soft 17 and 18.  For example: A, 2, A, A, A, 2, 4 is a possible a 7-card 12, then three more small cards make a winner.

But even if it’s only in the order of hundreds of billions to one, what is this actually worth?  The dealer will bust from a 7 thru A about 21% of the time anyway and roughly half the time your made hand will already win, or at least tie.  Roughly.  I really can’t try to think about how the deck composition after our ultra-low 10-card hand has come out might affect it.

So I’m going to approximate and just round down to zero.  You can be absolutely sure if I ever pull a ten-card hand in blackjack, there’ll be a screenshot coming!