Blackjack 3rd “loss” Analysis

So in the previous post I showed the frequency of different win-loss-pushes in a row. I demonstrated that there is a 50% drop in likelihood of a 2nd loss in a row and then another 50% drop in likelihood of a 3rd loss and another 50% drop by the 4th loss. After that the chart levels out with any further loss in a row being equally [un] likely. It also demonstrated that it is a bad idea to keep escalating bets beyond 4 due to this because though it is unlikely that one would lose again, at that end of the scale winning and losing are about equal likelihood (aka: no real advantage).

So the chart shows that the optimal inflection point is between the 3rd and 4th loss. So again used two programs to determine how frequently one hits on the 3rd try (after 2 losses in a row). Same rules applied:

Basic Strategy, no deviations.
6 decks
4 shoes

So since the charts got kinda messed up, the first bar is wins on "3rd try" (just had 2 losses in a row) the second bar is you just lost your 3rd hand in a row and the last bar (3) is you got pushed.

The reason I have 2 charts per app is because I was surprised by the difference between Mobilityware and BJAT. These two apps must be using different algorithms to get their "randomness". I will say that I have found MW to be somewhat streaky. Assuming BJAT to be more accurate you can see that on the second pass it "conformed" to the expectations. It is possible that the first run was an example of negative deviation and indeed I was cash negative for most of that run (was also up 12% at one point and I would have cashed out).

In the charts we can see that the win percentage on BJ Apprentice trainer falls on the low side of wins at 44.7 and 48.27% wins respectively. Admittedly I thought that to be pretty low given the previous charts. I cannot say how this would actually play out but you would “break even” in a give and take situation (assumings your gives aren’t doubles). If you’re fortunate, with a few BJ and doubles on your high bet you can come out far ahead.

Mobilityware showed a far more favorable win rate for the player with 57.14% and 57.8% win rate. This is a SERIOUS advantage and if it played out like that in a casino, one could expect to make a lot of money as that is way beyond the casino advantage.

The average between these two is 51.97% (52%) which is still an advantage over the casino.

Now I have not had practice play that resembled anything I saw at the casino. Some better, some worse, which I guess is about right so take these stats with the appropriate grains of salt and remember these stats are for short term play, I have no idea and have no intentions on how this would work out long term.

BlackJack Win-Loss-Push In A Row Stats

When you are not counting cards you are faced with a situation where you need to use some kind of sound statistical model to win money. Even when you are counting cards you are using a statistical model to approximate your chance of winning. As you may or may not know just because the odds are in your favor of winning a particular hand, doesn’t mean that you will actually win them.

I’ve recently acquired the skill of card counting and proceeded to have the longest string of losses than I ever had. The primary reason for this is that I did not understand that at high counts not only are YOUR odds high of getting “pat hands” and “blackjack” increased but so are the odds of the DEALER getting pat hands and blackjacks AND PUSHES.

So I had to go back to the drawing board. One thing I stopped doing as my earnings increased was “grabbing my winnings” when they were there. That is, I no longer was satisfied with a $50-$100 win for a session ($500 bank). I thought I should and could extend these sessions. It seemed to work that way in practice but at the table, ahhh..no.

Also I looked back at what I did when I did not understand or was able of counting. I ran (and still do) progressions. As indicated in a previous post, running progressions, particularly negative one can deplete your bank very quickly. However there are sound reasonings for why people do run progressions and make money off them in the short term.

Let me emphasize that I am talking short term. I read about players sitting for 20 hours or so. I don’t know how much bank they start with but I have NEVER sat at a BlackJack table for more than 6 hours total. I can barely go an hour before I have to pee. So what follows are relevant win-loss push stats that may be useful for those who cannot count but want to use some sort of statistical model for their betting.

Below you will find two charts. These charts are the results of playing 4 consecutive 6 deck shoes with cut card and dealer hitting on soft 17 while playing basic strategy with NO deviations. Essentially a no counting amateur who managed to memorize or follow BS.

Chart 1 shows the results playing MobilityWare BlackJack 5.5.1 on iPhone IOS 10.2. Chart 2 shows the results playing BlackJack Apprentice Trainer same platform.

What you are seeing are how often “back to back” events occur. Double downs are not considered two hands though one would want to consider the potential monetary impact of a double down loss. Successful splits are counted as double wins. Double loss splits are considered 2 losses in a row and a split split is considered a single loss and single win.

You’ll note that with both apps the odds of winning or losing two hands in a row is around 50%. That is if you’ve lost the first hand the chance of losing the second hand is 50%. You’ll note that winning or losing the third hand halves again the chances. Note that there is a leveling off beginning at 4 hands. There is very little statistical change between win and loss 4 and 8 in a row. This is why if you are playing strictly on win-loss statistics and using a negative progression it is in your interest to stop the bleeding at 4x. At 5x and beyond though the likelihood of losing again is low one has already entered the “damn near impossible” realm and anything goes ( and I have the losses to prove it).

So what does this mean to the basic strategy player with small bank? Well in my opinion, particularly for people playing with small bank (1k and under) you should use the 10-20% rule. When you are up 10-20% of your buy in, bail the table at the next loss and cash out your winnings. Then sit back down and go for another session and repeat. Why do I say this? Well while making these charts I flat betted and was up 100 to 150 on each game and then lost the majority of the winnings. In some cases falling into losing territory (usually on high counts shrug). So there IS money to be made even when flat betting but due to averaging out, the wins that generate that money is going to get wiped out by corresponding losses, you can see that in the chart, there are approximately the same number of wins and losses but losses OUTSTRIP wins in the long term even in this 4 shoe sample. So rather than hand back your winnings to the casino (which you’ll call “leveraging winnings”) cash it out.

That said, knowing these odds, you can (and should) increase your bets per stats. If you’ve lost 4 in a row and continue losing (and you’ve reset your progression right?) you can get to a “large win” if you keep following it. Same rules from counting applies though: Don’t over bet your bank. Keep your cool. One note though. A lot of the damage in negative progressions comes from doubles. You get say 3 losses out and then double on the 4th. If you chase that double by doubling and doubling again as is necessary to level out your bets you run two steps on the chart. I personally say to not chase a double unless it is your first or second loss, consider anything after that a loss to be recovered later if possible.

Also since flat betting can lead to profits, you may want to look at how often you’ve lost or won in a row and throw a larger bet out simply because the stats are in your favor (say, 3rd loss). Don’t blame me for any losses though.

If you count (or have a good eye for tracking when far too many low cards have come out) you can combine these stats and the count to modify your basic strategy play. For instance, on a ridiculously high count if you have a 13 facing a 7, there is a high probability that you will draw a bust card. There is also a high probability that the dealer has a 10 hole card. This means you’re likely to break ahead of the dealer if you draw and still see a 17 OR you’ll stand and the dealer has a 17. But on the chance that the dealer is not sitting on a 17, there is a high probability that the dealer will break on the draw. You might want to let the dealer take the risk rather than yourself.

Another example would be a 15 or 16 against a 7-9 with a high count. Basic strategy says hit the 15 against those and surrender a 16 to a 9. BUT again those high counts mean it’s likely you’ll draw a bust card (usually a 10 value card). Since you’re likely facing a losing situation anyway (stand and lose to a 17=19 or draw for an almost guaranteed bust) why not let the dealer take that risk? But now I’ve strayed into counting territory.

The point here is that Basic (and counting) are long term propositions. A lot of people are not playing for 20 hours straight or even 8 hours straight or going to a casino for an entire weekend. But they want to make money. Money can be made in the short term if you understand what happens short term. If you’re up by 10-20 percent, grab your money! The stats say that if you stay you’ll give it back. And consider this. If you have a disastrous start (something that happened during this test with the BJ apprentice software you have to come back from that before you can profit. So if you’re down 80 and need to get 50 to make your 10% that’s $130 you need to make. That hurts. So look at your down. If you dropped a LOT then you’ve experienced one half of the statistics, the rest will come back (unless you are REALLY unlucky). But when you get back up and you get a little profit, bail and come back. Money management will help you not dig too deep a hole but understand that for a BS player once you’ve gone halfway through your bank (buy in) it’s usually impossible to recoup during that session. It’s probably best to walk away and go home.