Deep(er) Learning from BlackJack Machine Emulations

I have been testing the "winning" Blackjack technique documented two posts ago... that is:

A Simple Winning Technique for Automatic Blackjack Machine Play

Here are two summaries of workable rules. NOTE WELL: There were things learned that render some of the prior discussion (in the prior post above and in discussion below) to be mistaken! I have not edited out and corrected the narrative for various reasons, mostly because I wish to record that some concepts need to be developed and improved by experience, in a gradual way. This is a small instance of such an improvement over time.

FIRST TECHNIQUE: this is a "known good" technique a bit more powerful and profitable than the 2nd Technique (stated below). It depends upon basically the same MMD (modified Martingale doubling) technique as the 2nd Technique, with different heuristic details, so to speak. It uses a minimum starting bet level of $3, along with detailed process stated as short rules that are (I hope) more simplified than the 2nd technique, also outlined below:

Beating Blackjack Machines - Summarized Technique

1. Use Basic Strategy as you play out hands with the machine.

   1. Details of Basic Strategy which governs hit/stand/double down/pair split actions can be found elsewhere in this blog, as well as being widely published on line and in books.

2. Start at $3 minimum bet level, with a total playing stake of $800

3. If you lose the (starting) $3 bet, double your bet.

   1. If you win, start again at step 2.

4. If you lose the doubled ($6) bet, continue to double your prior bet level.

   1. $6, $12, $24, $48, $96, and $192 are your progressive bet levels if you continue to lose.

   2. When you win, start again at step 2.

5. Continue the process (known here as MMD-- Modified Martingale Doubling), repeating steps 2 through 4 until you reach a "goal win" total of $40 or more.

   1. When you have attained "goal win" (or better) of winnings, then quit and d.s.e. (do something else) for at least 15 minutes.

   2. After 15 minutes of doing something else, you can feel free to start again and repeat steps 1 through 4, to another goal win of $40 or more.

6. If (not likely) you lose 6 times in a row, and lose the penultimate MMD bet of $96, then

   1. Quit and d.s.e. for at least 15 minutes.

   2. Feel free to start over at step 1 after doing something else for 15 minutes.

   3. Notice that your total loss is $189, less than one quarter of your original gambling stake of $800.

7. Accordingly, you would have to have an extremely unlikely run of multiple "lose-6-in-row" events before exhausting your total gambling stake of $800.

   
   

2ND TECHNIQUE, here is what I "know" as a good winning technique, stated as short rules, without specific proof, using a minimum $2 starting bet level:

Sustainable Model Summary-- Beating Blackjack Machines

• Use $2 starting bet level! (More on this rule later)

• If you lose the hand, double your bet. If you win, start over at $2 bet level.

• If you continue to lose, continue to double your bet level, 2/4/8/16/32/64/128. Use this modified Martingale bet doubling (known here as MMD) for at least 6 losses in a row before accepting a total loss-- and 7 times in a row would be "better" mathematically--However MM Doubling after 6 losses involves betting $256 on a single BJ hand, which you could well lose, and which anyway would when you win increase your net win in this session of play by just $2.

  • It seems more reasonable to quit a session of play, do something else (d. s. e.) for a while (approximately 20 minutes), and start a new session of play later (as an independent trial) with a starting bet of $2.

• Quit a given session of play when your profit level on this session of play is at $40 or more, or when you have experienced 6 losses in a row (as above described).

  • The lower $40-level-of-net-win keeps playing sessions short. Shorter sessions (playing fewer hands in a given session of play) allow less room for unusually long "losses-in-a-row" events to occur.

• After each session of play, do something else (d. s. e.) for at least 20 minutes, before starting a new session

• Count 5/V-5s in each hand. If you see 3 or more 5/V-5s in a hand, increase your next bet by $10 (in addition to the prescribed MMD bet level.

• If you lose an increased Count-5/V-5's bet level, do not carry that increased bet level into subsequent hands of a given session of play.

• Starting bet level of $2 bet is NOT optional, unless you can afford to drastically increase your total playing stake at risk to several thousands of dollars.

  • Note that attempting to use $3, or $4, or more for a starting bet level, you would at times have to be betting hundreds of dollars to net only $3/$4 dollars gain across several doubled bets!

  • To avoid this, use $2 starting bet and double 6 times in a row, ($128 maximum MMD bet level). Such a policy would allow you to completely exhaust your 6-in-a-row allowed losses 5 times (a very rare occurrence), while still retaining enough capital to enter a new game, after d. s. e. Note that this assumes an $800 total starting stake, rather than $600, which itself could be said to buy you "enough" safety against the risk of "gambler's ruin"; look that up with google if you are unfamiliar.

• Play MMD doubling along with counting 5/V-5s found in each hand and increase your bet for one hand only, when 5/V-5s count showed 3 (or more) 5/V-5s in the prior hand as it finished.

  • Increase the bet by only a single $10 increment added to the subsequent hand's bet level, whatever the MMD betting level is for that hand.

• Use a MMD level reminder card with a paper clip pointer, to indicate the next MMD betting level, in addition to a Basic Strategy Cheat sheet. Advance the paper clip pointer as you employ MMD, up to doubling 6 times in a row.

• Use Basic Strategy for Hit, Stand, Double-down, and pair splitting decisions, to play out each hand.

-------------------- [Prior discussion, with erroneous starting bet levels and more] -------------------

Modified Martingale Doubling (known here as MMD) does indeed allow one to create a pattern of steady "small goal wins". HOWEVER, at unpredictable intervals MMD produces a spectacular large loss that more than makes up for all the small gains. Naturally enough, and to be expected-- the house edge is still in play. In one example during experimental play, I experienced 10 losses in a row, with doubling! A huge net loss resulted, obtainable only by the trainer/simulator allowing (and myself using) an ability to "borrow" more total gambling stake.

SO. There are a couple of things ways to respond and potentially "fix" this: The first is to use "count-the 5/V-5's". Of course, that technique (also) would be overwhelmed by experiences like 10 losses in a row. AND a moment's consideration allows estimation of the odds of 10 losses in a row to be only about 1 in 1000. That is: the odds against 10 losses in a row are lower than one might naively expect!

Another technique is to keep track of "losses in a row" and stop playing altogether before the next single bet gets to be so high (that is, 2**10 or 1024 times the minimum bet).  SO, I experimented with MMD loss doubling capped at 64 for $4 starting min bet, and then (only for a short trial) of MMD loss doubling capped at $128 for $8 minimum bet level.

I have just tried that, with only one trial hitting as many as 6 losses in a row. I was able to turn "6-losses-in-a-row" into yet another routine-level win of $63. This was a victory. However, this appears to be a singleton (i.e. lucky) victory. In other trials, capping the MMD doubling level at six losses in a row, and losing at the last/highest loss level happened repeatedly, enough so that I was "stuck" with an accumulated loss that was not easily made up in subsequent sessions after D.S.E (doing something else) to create new sessions as independent trials.

ANOTHER ISSUE is that when playing Basic Strategy and attempting to count 5's/V-5's, I found it difficult to both count 5's and to keep track of where I was in the MMD progression.

Skipping a level without a loss for that level, (because I was distracted by 5/V5's count), and/or repeating a level both would tend to cause accumulating losses. I devised a "doubling tracker"-- simply an index card with the MMD betting levels listed vertically, with a paper clip "pointer" clipped on the card. Whenever I advanced bet money for the current MMD bet level to the betting circle, I would move the paper clip down to the next modified martingale doubled bet level, keeping track of where I was while I was busy executing Basic Strategy hit/stand/doubling/pair splitting moves and evaluating whether 5/V5's count justified "bonus amount betting".

• The "doubling tracker" can also be consulted to keep "losses in a row" in a serviceable way. Let's try to codify that supposition into rules and then try the rules by extensive emulator play:

• If starting at $4 min bet, we find ourselves faced with MM doubling to $128 level (i.e. 5 losses in a row) THEN

  • Instead of betting $128 (compounding the loss), return to $4 minimum bet level. Use MMD plus basic plus "count the 5/V-5's" to recover your loss.

  • If that does not work (another set of losses such that we do not recover the prior loss) THEN quit and do something else for a while.

  • If that does work, (i.e. you recover the loss and regain your original playing stake after doing something else) then resume MMD until you have a "normal" moderate profit $45-$65. With about 85% odds, you would succeed it that last part, I believe.

• If starting at $8 minimum, then avoiding 5 losses in a row puts you at $128 for your largest bet. Avoid MM doubling into a $256 bet level, that is.

  • Use a recovery strategy exactly as practiced for $4 min bet starting level, except you venture one level higher maximum bet before returning to $8 min level-- And of course you sustain higher losses with the same level of bad luck risk; with corresponding greater gains as one recovers and wins.

Okay. I am going to play the above model for a while, and report results with additional text below (in due time) ...

AND WHAT I FOUND: The house edge will out. I experienced MMD multiple loss runs repeatedly enough to overwhelm the more common, smaller win levels that MMD doubling yielded.

HOWEVER, there might be still a way to use MMD betting with 5/V-5's counting to yield Blackjack Machine wins. If one starts the doubling level at the absolute minimum bet level allowed of $2 and used a total stake able to absorb at least 4 "MMD disaster losses" (of 6 losses in a row), the gain level could be smaller, but positive more often than not.

ALSO, if one "takes profits earlier" (by accepting a lower common level session gain) then because of fewer hands in play for a lower, "common session gain", the chance for the more rare (higher odds against) MMD disaster is reduced. Perhaps such parameter changes in the model might find a "sweet spot" wherein common session small gains yield more than the occasional (rare?) MMD disaster loss. ALSO in the mix: increment the 5/V5 counts betting to select only more favorable situations for "bonus betting"-- i.e. only bet a bonus when 3 or more 5/V5's are seen in a single hand, and then only bet 10 bonus amounts (in addition to the MMD-controlled current bet level).

SO, I am going to play some more emulation trials, seeing if I might find such a "sweet spot" using a starting $2-level MMD (w/ count 5/V-5's) vs a stake of $600, AND (perhaps) $3-start-level MMD plus count 5/V-5's. Note that 5-loss MMD disaster loses only $126 cumulative with $2-level start doubling. Equivalent $3-level start doubling loses $189 after five losses in a row.