Hi All. Sorry for the delay in posting but it has been a long time since I've looked at redoubling and I wanted to make sure that no new bugs had been introduced into my software with respect to that feature. I also made some improvements to my chart generator. In any case, I'm happy with my latest results and ready to show them to you. I'm posting here because the questions were originally asked here and I don't think that the information is
overly sensitive. After all, part of this strategy has been available from the Wizard of Odds for many years now.
As far as I can see, the only difference between the game being discussed here and the one that Colin and I analyzed years ago is that this one has full early surrender. As a reminder, the rules as I understand them are 6D S17 DOA DAS SPL3 SA1 and redouble for the amount of the original bet (i.e. bet 1, double for 1, redouble for 1). Here is my strategy for this game if you can not double for less (more on that later).
https://gronbog.org/results/blackja...asic.6.s17.es.doa.das.rdo1.spl3.sa1.enhc.html
It was speculated above that the player edge for this game might be around 0.5% which is close to my figure of 0.55%. However, it's possible that we can do better. It turns out that, in this situation, where you can only (re)double or stand, it can be correct to double for as little as possible. The reason is that doubling for a very small amount is more like hitting once than doubling and, for some hands, hitting is what we would really like to do. Here is my strategy for the same game where we can double for less:
https://gronbog.org/results/blackja...c.6.s17.es.doa.das.dl.rdo1.spl3.sa1.enhc.html
Let me first explain the notation for redoubling:
- ds means that you can double for any amount, but you should double for as much as possible
- lds means that you can double for any amount, but you should double for as little as possible. $1 or even less if they have chips for it and will allow it.
- l(xx.x%)s means that you should double for less but only if you can double for
less than the indicated percentage of your
total previous bet. If you can't do this, then you should stand. For example, if you bet $25, and doubled for $25, then your total previous bet is $50. If you have 13 vs T, for example, If the cell says l(20.8%)s, you would double for less if you can do it for $10 or less, otherwise stand. Take a look at 6 vs T. The cell says l(1.3%)s. In order to make this redouble, you would have to be betting something like $500, doubled for $500 and could redouble for $1!
- d(xx.x%)s means to double for as much as possible but only if you can do so for
more than the indicated percentage of your total previous bet. This is important for this game where we can only redouble for the amount of our original bet. In particular, for A,7 vs 3, the cell says d(70.4%)s. In this game we do not make this double because we can only redouble for 50% of our total previous bet.
A few of notes:
- Notice that the strategy for redoubling when you can double for less becomes the same as for when you can't if in fact you can't. That is, all of the doubles for the full amount are available.
- Being able to redouble for less means that you make more initial doubles.
- Notice that the hands which we redouble for less are pretty much the ones we would normally want to hit.
- The player edge of 0.94% when you can double for less assumes that you can double for zero, which is a purely theoretical result. Your actual edge will be less than that and becomes worse as you are forced to double for more. It will be between 0.94% and the 0.55% given for the no-double-for-less game.