weaselman
Joined: Jul 11, 2010
• Posts: 2349
October 5th, 2010 at 6:02:39 PM permalink
Quote: mkl654321

The only question would be, what would be the expectation of the doubled bet when you CAN surrender, vs. the expectation of the doubled bet when you CAN'T?

The expectation of surrendering is better - that's why you want to surrender in the first place.
But you are right, we need to look at the expected value, not just probability (I knew, I was missing something :))

The probability that the dealer will bust when he has 8,9 or 10 is about 20%, making the EV of not surrendering 0.2*2 - 0.8*2 = -1.2, making the real benefit of being able to surrender after double about 0.3% - indeed, much less then I wrote initially, but still more significant than your estimate.
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mkl654321
Joined: Aug 8, 2010
• Posts: 3412
October 5th, 2010 at 8:22:21 PM permalink
Quote: weaselman

The expectation of surrendering is better - that's why you want to surrender in the first place.
But you are right, we need to look at the expected value, not just probability (I knew, I was missing something :))

The probability that the dealer will bust when he has 8,9 or 10 is about 20%, making the EV of not surrendering 0.2*2 - 0.8*2 = -1.2, making the real benefit of being able to surrender after double about 0.3% - indeed, much less then I wrote initially, but still more significant than your estimate.

But my estimate was on the effect of the ability to surrender after doubling on the OVERALL GAME. Surrender-after-double is only significant on those hands where you a) double b) against a strong dealer upcard and c) you make less than 17. So let's use the 22% bust figure, which is fairly close to the overall chances of the dealer busting with upcards 8-A. Let's also, for shorthand, call the a)b)c) hand a Double Surrender hand, or a DS. If you can surrender a DS hand rather than holding your breath and hope that the dealer busts that 22% of the time, then that increases your expectation from 22% to 25% (by surrendering, you achieve the same expectation as if you had a 25% chance of winning). This means that you gain 3% of those bets where you double and make a DS hand, which increases the overall expectancy of doubling down against a strong dealer upcard.

So a 5% increase in the overall expectation of a bet that you don't make all that often (doubling against an 8,9,10, or Ace), and only of a SUBSET of the results (you make a total of less than 17) you achieve, is not all that significant. I don't know how often you get dealt a double down hand, but I would guess that you find yourself doubling down only once every fifteen hands or so. And you make less than seventeen (a DS hand) less than half of the time--for instance, when you double on hard 10 or 11, you only make 16 or less with five of the thirteen possible cards. So 1/15 of the time, you double, and 5/13 of that time, you make a DS hand, and you save 3% of your bet by doing so. 5/180 is about 0.03. So 3.0*0.03= 0.09, or about a tenth of one percent. Of course, this calculation assumes that my guesstimate of 1 double every 15 hands is correct. But even if it's really more like one in ten, that's still only a gain from DSing of 0.15%.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
Mikey75
Joined: Mar 1, 2013