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http://www.bjstrat.net/cgi-bin/cdca_web.exe

I compared the strategy given there to what the Wizard has on his Charlie page:

https://wizardofodds.com/blackjack/strategy/charlie.html

Here's some differences I found (with all computations I used 6 decks; sorry if I made any errors):

Hit/Stand: This isn't an error since the Wizard assumes S17, but in an H17 game 13 vs. 3 should be hit only if one card away from an auto-winner and 16 vs. 3 should be stood on.

Doubling: The Wizard's chart assumes a 5-card Charlie; with a 6-card one the only changes from regular BS should be don't double A2 vs. 5, and double A4 vs. 4 only with H17.

Splitting, 5-card Charlie: The differences with 22, 33, and 44 are probably because the simulator I used allows for Charlies on post-split hands but the Wizard's calculator didn't. According to the calculator, with DAS 22 should be split with 4-7 up and 33 with 3-7 up; without DAS split 22 only with 6 up and 33 with 5-7 up. The calcuator doesn't show any changes from regular BS on 44-TT. With AA it matches what the Wizard says in that you shouldn't split AA vs. A, but also shows that AA vs. 9 or T should be hit as well with an asterisk if resplitting is allowed (I haven't figured out what that means; I guess it means that you should split if RSA is allowed and hit if it isn't).

Splitting, 6-card Charlie: Once again, the differences are probably because of the differences in allowing Charlies after splitting; on the calculator I don't see any changes from BS.

The easiest way to see that something is wrong is to look at 16 vs 6, one card away from a Charlie. Wizard's chart says hit. With an infinite deck, your chance of winning by hitting is 5/13 ~= 38.5%. Your expectation on a hit is 5/13 - 8/13 = -3/13 ~= -0.23. Now look at Appendix 1, where he gives the expected return for standing 16 vs 6 in an infinite-deck S17 game as -0.15. Standing is better. The same analysis shows that hitting 16 vs 4-5 and 17 vs 2-3 is wrong.

I would distrust the rest of the chart, seeing that some of the values are wrong, and other values almost certainly depend on them.

Incidentally, I've done a little analysis on single-deck six-card Charlie strategy, like you find in many video blackjack machines. If any book covers this, I'm not aware of it (but would like to hear about it!) The strategy is much more conservative. For instance, not only do you stand 16 vs 6, but you also stand 15 and 14 vs 6. By the time you have a 5-card 14, you're probably looking at a +6 count and the dealer's chance of busting is close to 50%, rather than the 42% at a neutral count with infinite decks.

Quote:fivespotI'd been meaning to post about the Charlie strategy. I believe Wizard's strategy is just wrong

Uh Oh....

Quote:fivespot

The easiest way to see that something is wrong is to look at 16 vs 6, one card away from a Charlie. Wizard's chart says hit. With an infinite deck, your chance of winning by hitting is 5/13 ~= 38.5%. Your expectation on a hit is 5/13 - 8/13 = -3/13 ~= -0.23. Now look at Appendix 1, where he gives the expected return for standing 16 vs 6 in an infinite-deck S17 game as -0.15. Standing is better.

Five Card Charlie Strategy gives a different rule for When to Hit

You have 4 cards that total 16 and the dealer is showing anything but a 4,5 or 6.

As you pointed out it is only in these two cases using infinite deck EV's

Dealer 2, EV is -0.292783727 if player stands

Dealer 3, EV is -0.252250229 if player stands

In both cases the EV is less than -3/13 = -0.2307692

So your reasoning seems sound.

Good job fivespot.

Something does seem a little off about. It is hard to figure how to play certain situations based on the chart. Then again, I've only seen one land casino with 5-card charlie in my life, and I've been to A LOT of casinos. I don't play online.Quote:fivespotI'd been meaning to post about the Charlie strategy. I believe Wizard's strategy is just wrong - it's not a matter of six decks vs infinite decks, as he suggests.

Quote:fivespotThe easiest way to see that something is wrong is to look at 16 vs 6, one card away from a Charlie. Wizard's chart says hit. With an infinite deck, your chance of winning by hitting is 5/13 ~= 38.5%. Your expectation on a hit is 5/13 - 8/13 = -3/13 ~= -0.23. Now look at Appendix 1, where he gives the expected return for standing 16 vs 6 in an infinite-deck S17 game as -0.15. Standing is better. The same analysis shows that hitting 16 vs 4-5 and 17 vs 2-3 is wrong.

I would distrust the rest of the chart, seeing that some of the values are wrong, and other values almost certainly depend on them.

Blackjack Strategy for Charlie Rules says ..you have 16 to a Dealers 4, 5 or 6 if so then you should stand your hand. ...If you have a hand of 17, 18, 19, 20 and the Dealer is showing 2, 3, 4, 5, 6, 7, 8, 9, 10 or an Ace then you should stand.

The chart is certainly wrong because it is a simple matter of comparing expected values. Probably nobody ever noticed it since I have never seen credit given for a Charlie unless they take away something much more valuable (like payouts for blackjack). At that point it seems kind of stupid to play a game correctly where the rules are stacked against you.

I've heard of short-term land casino promos involving 5-card charlie, but never been in on one of them myself. However, 6-card or 7-card charlie is a rule on every video blackjack machine I've seen.Quote:teddysThen again, I've only seen one land casino with 5-card charlie in my life, and I've been to A LOT of casinos.

I missed the golden age of card counting, and anyway, I hate playing the game of trying to figure out which bets some bozo in a suit will or won't let me make. So I mostly play machines instead of tables. Mostly video poker, but on those rare occasions when there's a profitable opportunity with video blackjack it's a pleasant (and low variance!) alternative. Thus my interest in getting to know Charlie. :)

Quote:fivespotI've heard of short-term land casino promos involving 5-card charlie, but never been in on one of them myself. However, 6-card or 7-card charlie is a rule on every video blackjack machine I've seen.

But, video blackjack machines usually pay 1:1 on blackjack. The reason people play video blackjack is to get free drinks at the bar. It seems really stupid to take the time to learn correct strategy on 6 or 7 card charlie since it is worth so little overall.

I doubt that you will find a casino stupid enough to give the player an advantage by permitting a charlie rule.

I only answered this question because the mathematics intrigued me.

I can find the house edge effect(+1.46%) and lt's strategy(https://wizardofodds.com/games/blackjack/rule-variations/automatic-winner-charlie-rule/) for 5 card charlie( 5 cards unbusted hand autowin 1 unit !)

However, what is the strategy for 5 card charlie autowin 0.5 UNIT ?

James