The Lucky Donut

I should probably admit that my "new book" is not actually that new any more.  I had almost completely finished writing this one over a year ago. 

Call me a perfectionist if you like, but I think procrastinator is probably more accurate.

I had to jump through a few hoops (and pretend to be American) to get an ISBN so that Amazon might list it, but when it came to it this week when I decided to finally publish the book there wasn’t much more I had to do than copy a chunk of text onto the copyright page and add a barcode to the back cover.

So, before I have chance to put it off any longer, may I proudly present: The Ultimate Video Poker Pocket Book.

It’s a grand title for something so small – and with such an unimaginative cover – I’m sure you’ll agree.

Furthermore, while I’m proudly trumpeting the arrival of a book I’ve written about video poker, it’s fairly easy to see that I’ve not actually had to write all that much at all myself.

In total, I wrote 10 (tiny) pages and I got a computer to create the rest.  Although, to be fair, there was quite a bit of work involved in doing that, not least of which was teaching it how to typeset everything just the way I wanted.

The end result is, in my completely objective opinion, an essential collection of video poker strategy charts and pay table data, all compiled into one very handy, very compact little book – it’s about the same size as a postcard.

The idea of the book is that you don’t just have one basic strategy chart to take to the casino or for playing video poker online – you have lots of slightly different ones.  Then, regardless of which game you decide to play and how the pay table is set, you can be sure that you’re playing optimally and making your money last as long as possible.

The concept evolved from an ever-growing stack of strategy cards I’d created for myself, held together in the corner with a split ring.  Rather than just carry a general strategy for, say, Jacks or Better, I wanted to make sure I was playing correctly if I found a machine that offered a different payback to what I was used to.

For example, the Stratosphere casino used to have JoB with a 10/6 or 9/7 pay table, which is even better than the "full pay" 9/6 game I usually like to play.

In this notation, the first number represents the payout (as a multiple of your bet) for a full house and the second is the payout for a flush.  On the 9/7 game, the value of flush draws (and straight flush and royal flush draws) goes up compared to 9/6.  Whereas the 10/6 version has a meatier full house payout, meaning that pairs – and even just high cards – become more valuable compared to draws.

The optimal strategy doesn’t change wildly, but it does change.  Although the 10/6 and 9/7 games had a positive expectation (and the casino advertised this fact loudly), to get the maximum payback it was necessary to adjust the way you play according to the pay table.

Sadly, these games died a death several years ago and never resurfaced.  Their pay tables didn’t even make it into the book (I concentrated on profiling the most popular games that exist today) but the same principle applies to any situation.

If you usually play 9/6 Jacks or Better and know the strategy well, but one day the only game you can find is a 7/5 or 8/5 machine (typical on the Las Vegas Strip) you know the payout is going to be worse than you’re expecting – but it’s going to be worse still if you don’t adjust your strategy to account for the short-paying hands.  

As the payback for the flush and full house gets smaller, the value of a straight draw increases.  Not by enough to affect most decisions, but some marginal hands should be played in a different way.

For example, if you were dealt 99TQK, it would usually be correct to hold the pair over the straight draw, but with a 7/5 pay table the optimal play is to draw to the straight, or try to pair the queen or king to make a winning hand.

Well, in truth the optimal play is get up and find a better game than 7/5 JoB, but sometimes that’s just not an option.

How do we know this is right?  Computer says so.

You’re just going to have to trust me on this, but the strategies have been thoroughly tried and tested on real games as well as on simulators that tell you when you’re making a mistake.

Heck, I’ve been using this book for 18 months and it’s prototype for years before that.  If there were an error, I’d have found it by now.

Here’s how the book looks when you hold it open on a particular page.  If you have really good eyesight (or just the initiative to click the image to enlarge it) you can have this strategy for free! 

When held this way round, the upper page shows various pay tables for one type of game.  In this case it’s Bonus Poker.  One of the pay table variations is shaded and as you flick through the pages the shaded column moves.  When you’re looking at a shaded pay table that’s the same as the one on the game you want to play, the strategy on the lower page in the book is the correct one to use.

The book also lists payback percentages, so you see how your chosen machine compares to pay table variations of the same game.  This allows you to shop around and find the best games more easily.

Or if you already know which game you’re looking for, the shaded bar along the edge of each page contains that information and makes it easy to find.

If I may say so myself, it’s quite ingenious. 

So, how do you read the strategy charts?  The book explains in a bit more detail what all the abbreviations stand for (you can read the whole introduction in the preview, here), but once you see what’s going on it’s logical and quite straightforward.  Here’s an example.

Suppose, when playing Bonus Poker with an 8/5 payable (corresponding to the picture above), you are dealt: 7s 8h 8c 9h Jh.

Your hand contains one pair, a four card straight draw with one gap and a three card straight flush draw with one gap.  However, the draws each also contain a jack, which is considered a "high card" as this game pays out for pairs of jacks or better.

The relevant sections of the strategy chart are items 15 and 19, enlarged here:

Item 15 is "1P (2-T)", which means "one pair (as long as it is between twos and tens)".

Item 19 groups two similar types of hands into one item, and the second one is our draw.  "3SF (8-Q) 1GAP 1HC" translates as: "A 3 card straight flush draw (having all cards between 8 and queen) with up to one gap allowed, but it must also contain at least one high card".

Once you know that SF is a straight flush draw and HC stands for "high cards", you can read the chart very quickly. 

The hands are listed in order of their expected return, with the most valuable first.  So the optimal play in any given situation is to hold the cards that correspond to the highest ranked (i.e. lowest numbered) item on the strategy chart that features in your hand.

So this tells us that your pair of 8s is a better hold than 8-9-J for a possible straight flush. 

If a combination of cards isn’t on the chart, you don’t hold it.  The inside straight draw (7-8-9-J) in your hand doesn’t make an appearance – it would be represented as "4ST 1GAP", or possibly "4ST 1GAP 1HC" if having the jack made a difference.  It’s correct to hold an inside straight draw in some video poker games, but not this one.

The only other listed hand you have is "1HC (J)", which is way down the chart at number 32.  The pair and straight flush draw are both better holds than just the single high card.

This may all sound a little dry and the book is certainly not going to be to everyone’s taste.  It’s designed to be a useful companion, not something you’ll want to read cover-to-cover.

I’ve also realised from how long this post ended up being that it’s going to be quite a difficult sell.  If you’re still with me this far, you probably deserve a medal.  I need to work out how to explain what the book is all about (and why you need 80 different strategy charts in your life) in a couple of sentences!  

But at least I’m using a publishing on demand service so if nobody buys it, I won’t have piles of the thing sitting around gathering dust…

You can buy The Ultimate Video Poker Pocket Book from lulu.com: 

This is pretty sweet – it’s a mobile phone optimized version of the Harrah’s web site:

I know everyone’s doing it these days, but I hadn’t seen this before.  Harrah’s web site has always been way ahead of the game for communicating with players and their mobile version is no exception.

The lightweight site has virtually everything you get on the full scale web site, except it doesn’t bombard you with pictures of Bette Midler or adverts for the latest poolside debauchery.  You can access to your Total Rewards account – including all your offers, and it lets you make reservations.  Very nifty.

The site address is mobile.harrahs.com and I’ve bookmarked it already.

It actually took me a while to find the address for this even after I knew it existed. I only came across it through their iPhone app, iSpin, which is a Harrah’s branded slot machine simulator.  You can actually choose how you want it to look from 8 of their casino brands.

The game itself is OK I guess.  Reels spin and you win or lose fake money.  Of course it’s rigged heavily in the favour of the player to make you think you’re eternally lucky, so when it’s a close call on whether or not to take out a third mortgage to go to Las Vegas with, you’ll think back to some happy memories of pretending to gamble on your phone and decide that you can’t possibly lose.

In fact this game lets you hold up to two of the three reels to increase your chance of winning.  As there’s a prize for just one cherry on the pay line, all you have to do is wait for that symbol and hold it indefinitely to get at least a 100% return on investment on every spin.

Needless to say, there’s no actual casino slot machine that plays this way. 

There’s a few annoyances, like it plays irritating casino background noise which you can only turn off once you’re into the game.  So if you were already listening to something on the iPod, it stops when you launch the app.  I hate that.

The thing crashed on me a couple of times already too, so it’s not that stable.  But it does a fine job at helping you to kill a few minutes, and I guess that’s what it’s there for.  A free play slot game was always going to have a limited lifetime for me.  I was really just curious as to what they were giving away and how they were using it for casino marketing.

It was the Total Rewards integration that really caught my eye though.

I thought that was interesting.  A Total Rewards app for iPhone?  Even if you have to access it through a slot machine game, it’s still a pretty good idea.

Unfortunately, this is the extent of the information you can get from the app.

Then the orange links take you off to the mobile site on the web where we started, except that the site is irritatingly locked in landscape mode whether you like it or not – and you have to log in again.  Forget that – just to skip the game and go straight to mobile.harrahs.com.

The only other thing of note about this app is that it asks for the iPhone’s location at start up.  This has absolutely nothing to do with the game or anything else in the app.

Big Brother at Harrah’s is watching you.  They not only want to know that you have downloaded and run their app, they also want to know where in the world you are.

They probably just snagged your phone number too.

Here begins the possibility of the most unlikely of career changes for me.  On Friday, I was hired to be the co-presenter on a pilot TV show.

It’s not the first time I’ve been on TV, but it is the first time I’ve been The Talent.

OK, so that’s a bit of a stretch.  But there I was, looking into the camera, sitting alongside someone who had actually done this kind of thing before, spouting on about blackjack.

Tonight, Matthew, I’m going to be a television gambling pundit!

How did this come about?  I’m still not really quite sure.

I’d been asked to write a series of articles about various casino games for a new area of the Poker Channel’s web site.  It must have been about this time last year that I was working on it, because I remember during the summer trying to grab as many game rules leaflets as possible from every table game in passed in a Las Vegas casino.  I now have a drawer full.

I began to write and started sending articles to the editor, whose subsequent departure from the company was timed so perfectly that I’d completed 17 of the 20 pieces he’d asked for before I found out that the new casino section was no longer a priority since he left and nobody else knew what I’d been working on.

Months passed, and eventually I decided to start hassling someone to see if there was any chance I they still wanted to use my work, or if it would instead become part of my yet-to-be-published “Luckydonut’s Awesome Guide to Gambling”.  That’s obviously a working title, but it has potential.

It turns out that somebody read my stuff and quite liked it.  Next thing I knew, I was invited to a meeting at their offices to talk about a TV show they were developing about blackjack, and really that’s as much as they told me before I got there.

I thought I might get some writing work out of it, but when I got there they’d already penciled me in as Charlie Brougham’s sidekick on the show.

I don’t watch any sport on TV so I didn’t know who Charlie was, never mind how to spell his last name.  It’s B, R, O, then a bunch of letters that don’t make any sound, and an M.  And they say English is a difficult language to learn.

When we first met, Charlie asked me what I did and I struggled to come up with any kind of answer that justified my being there.  “I’ve written some bits about blackjack for the web site” didn’t seem to cut it, even before I’d (I thought, politely) asked him the same question.

Next time I’m introduced to someone down there my reflex question is going to be, “Haven’t I seen you on the telly?”.

The next time I met Charlie, he’d ask me the same thing again – in front of the camera.  Fortunately this time I knew it was coming and had prepared an answer.  In the script, it went like this:

I’ve been a recreational gambler for as long as I can remember, and I’ve played and studied the strategies for just about every casino game you can think of.  I’m a bit of a maths geek and I’ve worked with computer software, so I’ve used that to analyse games and test various strategies to help me prove or disprove various theories about how to play casino games.

In reality it was a bit more stammery, but the same idea. 

As the idea of the show is to make money for a casino sponsor (in fact, the programme would be classed as an infomercial so that it can push the casino product as hard as possible) I thought it probably wasn’t appropriate to talk about bonus abuse and how I usually only play blackjack when I know the odds are heavily in my favour.

I wrote a few more set pieces about why blackjack is great, why you should never take insurance and some common mistakes to look out for, but the rest of the material was the two of us talking about blackjack hands that were being played out on screen, with me occasionally forgetting things I was meant to know, like whether or not you’re meant to double down on soft thirteen against a dealer’s four.

I’m told I did just fine.

However, I did come to realise that nothing is ever bad in TV land while the cameras are rolling.  If something’s not quite right, it’s “great” and if it’s a complete clusterfuck then it’s “fine”.

For example, “that was great, but we’re going to do it one more time, and try not to look so much like a rabbit in the headlights when you look at the camera”.

Or, “that was fine, but can we go again, and if Chris could remember what he was going to say that would be great”.

Well, eventually we got through it.  Editing and post-production will take about a week, and they’re going to send me a DVD when it’s done.  I doubt I’ll be allowed to upload any video, but my friends on Facebook will probably notice a new profile picture.  I’ll be quite disappointed if there’s not a usable screenshot with the caption: “Casino Expert”.

It was only a pilot so I don’t know whether the show will ever be aired, but if I’m going to be on the TV I might just mention it…

What’s wrong with this picture?  I’ve taken the liberty of enlarging the relevant text (or you can click to view the full original screenshot).

Balance £3.  Which means I have insufficient funds to place a £2 bet.

Let me try to take a stab at explaining what kind of logic is needed to come to this absurd conclusion.

Three Card Poker requires you to place an additional bet equal to your ante if you want to play the hand.  You can fold and forfeit the ante – but if giving up without a chance is only option you wouldn’t start the hand in the first place.  So in fact this £2 bet (including a £1 “pair plus” prop bet) actually needs me to have £3 in my balance to play it.

Which, it appears, I do.

[Side note: This is different to blackjack, where the game will never stop you from dealing a hand if you don’t have enough money to double down or split a pair.  You are at least able to complete the hand and stand a chance of winning something without using these options.]

However we already know that Gala suffers from fraction-of-a-penny rounding errors.  It’s not too much of a stretch to imagine that their bodgeroonie of a cashier system actually thinks my balance is very slightly below £3, but close enough to it that it is rounded up when displayed.

It’ll be some number like £2.999999995673, so that when asked “does he have at least £3?” then answer will be “ooooooh not quite”.

I see this kind of rounding error fairly often when working with decimal numbers.  It’s because computers suck at fractions.  Everything has to be stored internally as some representation of a power of 2, so only fractions with a denominator of 2, 4, 8, 16, etc can be stored exactly.

When working in hundredths, that’s just 4% of all numbers: those ending in .00, .25, .50 or .75; everything else is going to be converted to a (fairly long) decimal approximation; close, but not precise.  However, if you know that it happens, it’s not that hard to deal with.

Notably in the poker and casino operator APIs I’ve worked with, you don’t need to worry about this.  They have always stored and returned the player balance numbers as a whole number of pence or cents.  It makes it pretty easy to accidentally conjure money out of thin air – you just have to forget to divide by 100 one time – but it means that there are never any fractions of a penny floating around the system to go wrong.

In fact, some poker networks even store and return your player points balance as a whole number of hundredths of a point.  I guess they really don’t want to give much away!

My assumption is that Gala’s cashier system stores the casino balances as pounds and pence – a design decision that has side effects they either don’t know about or don’t care about.  For a system that handles real money transactions this is, frankly, a bit poo.

And if anyone from Gala actually reads this: yes, I could do (and have done) better.  Let’s talk.

Anyway, there’s more.  I really can’t begin to explain what the hell is going on this time.  The dealer’s cards were dealt, briefly flashing face up – but too quickly for me to remember what it showed.  They flipped over as soon as they were dealt, and then the game announced the apparent straight flush for the dealer you (don’t) see here.  Like I’m just meant to believe that?

“NaN” means “not a number”.  Or, in English, “something fucked up”.

Isn’t it great to know that when the game software has a glitch, the default behaviour is to give the dealer the very best hand possible?

Online gambling… probably rigged… yada yada yada.  I had 13 straight roulette spins landing on red.

Unfortunately I didn’t record the action itself, but I made this video of scrolling through my session results history afterwards.  Just hit the play button and count along.

It’s like thousands to one against.

To be more precise, 8191-1 for a streak of either colour, or 4095-1 for either streak (because I’d still be writing this if it had been 13 blacks).

It’s not astronomical odds, but it’s enough to make you sit up and take notice.

Also, I was betting on red, even, low.  Only five numbers lose everything: 29, 31, 33, 35 and 0.  Losing 3 times in a row is a 404-1 shot, yet that’s what happened right before the 13 reds: 31, 31, 0.

Also, if you didn’t notice, the last 7 numbers were red and odd.

Draw your own wild conclusions.  Conspiracy theories are always welcome.

It’s time for another randomly-generated-by-computer-using-a-secret-magic-formula virtual game from Sporting Index, which I’m only playing because they promised to refund up £50 of my losses.

To qualify for the refund, I have to place 10 or more bets at a minimum 20p per point stake.  After grinding through the first 9, I was £5.43 up.  Reasonable, but not enough to make it worth quitting just yet when I was in a situation where I could place a bet worth up to £55.43 and have it cost me no more than £5.43.

I don’t actually know where I should draw the line here.  Free money in the bank is good, but the chance of a better return for almost no risk is obviously attractive.  I think if I’d won £20 before qualifying for the refund, I’d probably be bottling it and taking their money even though it’s almost certainly in my favour to keep playing.

If I knew how the game worked, I could make an informed decision on how best to play this bonus through, but when the game is themed to look like a real world event, yet the outcomes are calculated in a way that you’re not meant to understand, you just have to trust that it’s not completely rigged.

I’m pretty confident that Sporting Index would not be associated with an outright scam, and although the game is surely very juicy for them, I’m assuming that it has a house edge somewhat smaller than 90%.  In which case letting my fiver ride is a good play.

The game in question is a random number generator painted to look a bit like the stock market.  You get to pick from three made up currency exchanges, each with its own degree of simulated volatility.

Then you can bet on one or more of the following markets.  I’ve condensed the display down after selecting a direction for each one to show the best and worst case scenario for each bet.

There are two distinct types of bets here: ones with a small downside and a large potential upside, and those where the swings are roughly the same size in either direction.

Of course, to win big money from any spread bet you need an extremely unusual event to occur.  Usually the result will be fairly close to the spread itself, resulting in a (relatively) small win or a small loss.

This is not great for exploiting a net loss refund offer.  Ideally we want to take one shot where we either lose the maximum (in this case lose £55.43, ending up with a net loss of £50, which will be refunded in full) or win something significant.

To play out the promotion, I decided to take the highest price bet.  Lowest price or even swing would have pretty much the same effect, but it just felt right to be cheering for the imaginary graph to be rise upwards rather than downwards.

With a stake of £2.21 per point (maximum risk: £55.25, maximum win: £828.75) and buying the market at 5025 here’s what happened:

Yeah I couldn’t work it out either.  It’s the blue line that matters, but even so… I had to let it tell me the result and trust that it was right.  Apparently I lost £30.94.

Looking at this chart a little bit closer, it was almost impossible to pick a winner this time.  The swing on the green line may have just got there, but I don’t think any of these graphs moved enough to cover the spread in either direction.  From the house’s point of view, it’s almost as good as a roulette wheel throwing up a zero.

It’s not all over though.  I could still have another £24.49 of losses refunded, so although the chances of getting back into the black were slim there was nothing to lose by taking another shot.

Same bet, slightly cheaper.  Buying the blue line for 98p per point: maximum risk £24.50, maximum win £367.50.

Awesome.  Lost another £17.64.

It’s not actually the extent of the downward plummet that’s bad for this bet, it’s that the graph never went much above its starting value. But the extreme downswing does rub it in a little, and it means that if I’d put money on either lowest price or swing – the two other candidates for this bet – I’d have been back in the game.

So, one more last, desperate effort.  Could I climb out of a £43.15 hole with just £6.85 left to play with?

Maximum loss: £6.75, actual loss £6.48.  That would be a no then. 

Gala.  Giving away money again.  This is not how casinos are meant to operate.

I deposited £10 for today’s bonus and it didn’t work.  So I tried transferring the money via my poker balance to see how much they’d sting me on the exchange rate.

I started with £38.22.

I transferred £20 to poker, which was converted to $30.62.

Then, I wasn’t sure whether the amount to transfer back was in pounds or dollars.  I entered “20” in the currency-less field and pressed “go”.

That meant $20, apparently, which converted back at £13.07.  Then I transferred the remaining dollars back to pounds.

I made a penny.  In fact, I made two.  After I noticed this had happened, I had to try to reproduce it to get the screen grabs above.

I’ve contacted customer support about this.  While the idea of making a bit of money Office Space (or Superman III) style is attractive, PMITA prison is not so much.

EDIT: Bizarrely today my balance shows as £38.22 on the homepage and £38.23 in the cashier.  Looks like they are storing balances internally accurate to fractions of a penny, then rounding differently in different places.

Not content with giving away money through three very playable bonus offers every week, Gala have just announced the following change to their cashier system that’s going to cost them even more:

Improvements to the “Cashier” function will display funds within 2 wallets – a Casino/Sports balance and a Poker balance.  [ … ] We’ve just made things easier for you – and there’s no need to transfer funds from one wallet to another!

If you want to apply for one of our bonuses, please make sure that you enter the bonus code when depositing, as you will no longer be able to transfer funds and enter the bonus code at that point.

Until now there were three separate balances; Casino and Sports both in pounds and Poker in US Dollars.

Admittedly, their cashier has always been a little clunky, so any change that results in players needing to use it less often is probably a smart move.

Now rather than keeping my balance in Gala and simply transferring money back and forth, entering each daily bonus code to qualify for that chunk of free money, I’m going to have to use a debit card several times every week.

Although the option to enter a bonus code still seems to be available for transfers between Casino/Sports and Poker, this will involve an exchange into US Dollars and back again and, inevitablly, the punter will pay commission both ways.

The more attractive option is to make a £10 qualifying deposit on Friday for Blackjack, one on Saturday for Roulette and another on Monday for Three Card Poker, then withdraw it all after playing the Monday bonus.  Rinse and repeat.

It costs Gala nothing to transfer money from one virtual pot to another, but as soon as a bank is involved they’re going to be paying a fee with every transaction.  For gambling transactions, those fees are pretty steep.

So while I’m sure it was their intention to encourage players to put money into their accounts in exchange for the bonus, what they’ve actually ended up doing is paying four lots of transaction fees in addition to giving away an expected value of about £22/week.

My main worry is that their systems will be set to detect repeated deposits and withdrawals and flag them for inspection – whereas shifting money around between their online accounts would not arouse any suspicion.

I’ll still be making hay while the sun shines though, and if you’re not already taking advantage of these bonuses, get them before Gala works out how much they are costing!

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!