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.