Not doubling against dealer 2,3,4 at high count.

Some while back I posted that in order to reduce variance, and the risk of having to go home early having lost my entire session pot, I didn't double down against a dealer 2,3 or 4 at high counts where I had a "big" bet out. I was pelted with electronic rotten fruit for even suggesting such a thing.

As a result of a PM exchange with Flash, I've made an attempt to calculate roughly what the cost/loss in profit is for doing this, and whether in fact I am tossing a big chunk of my EV down the pan as others have suggested. Before discussing the numbers though, I'll reiterate that I'm not a particular maths head and don't want to turn this into an exercise in getting stuck into a heavy round of statistical analysis. Also, I play for recreation only at low stakes, don't play with a fixed bankroll and usually visit the house of chance with around 40-50 units in the knowledge that on occassions I will lose the lot (although it hasn't happened yet).

I've attached a spreadsheet with some numbers on it that anyone is free to peruse and I'll appreciate any comments that help me fine tune the figures. I've done three calcs, all pretty rudimentary and with the aim of pointing me in the right direction rather than providing a precise answer. I don't have a sim which would have been the simple answer - run a billion hands for applying and not applying these plays and take the overall win amount one from t'other to arrive at a pretty accurate figure for the loss in profit. All three calcs have been based on the frequency that these plays are likely to be made (taken from Don Schlesingers Blackjack Attack) and multiplied by the frequency of TCs +3, +4 and +5+ - they add up to almost 8% so I'm satisfied these are in the right area.

Method one.
Simply calculated the frequency that these hands will come up, and multiplied these by the betting unit, unit value and approximate %age advantage at each true count. Calculated the difference in profit from hitting and doubling down and took this as the cost of applying these plays. Divided by 70 to get the approx cost per hour etc.

Method two.
Used the cost of play chart for OTT 6 deck game (one we have here in the UK) that BS is based upon to determine the profit/loss difference between doubling down and hitting for each play. I've adjusted these figures by multiplying them by 1.15, 1.20 and 1.25 for TCs +3, +4 and +5+ respectively as a weighting to allow for the plus TCs - this opens up the gap between the hit and double down cost to give an increase to reflect the better long term returns of DD over H. 9v2 shows as a neg figure as OTT BS says hitting has a better return than doubling down, but the effect is pretty insignificant, so I've left it in for consistency.

Again, I've tallied the total loss in profit and divided this by 70 hands per hour to arrive at a cost per hour of adopting this strategy.

Method three.
Based on the fingers in the table in Blackjack Attack that shows the long term cost in cents per $100 bet for deviating from BS, I have calculated the loss in profit on these plays and again calculated the cost per hour. I don't know how DS calculated these figures, or what deviating from BS refers to; ie not doubling down but hitting or not doubling down but standing - for this exercise I've assumed the former.

I appreciate that none of the calcs above will provide a definitive answer on which to bet my pension, but the worst case scenario amongst the three (method 2) indicates that the longer term costs of not doubling against a dealer 2,3,4 at TC+3 or higher is less than £1 an hour, based on 70 hands an hour. Bearing in mind the number of units I have at my disposal when I play, this seems a reasonable cost to swallow to reduce the risk of not tapping out and having to make the 50 mile drive home shortly after arriving at the felt. Like everyone else, my biggest losses have been at high counts.

Again this is about risk and return. I found an article authored by James Grosdean and Prevan Mankodi at BJMaths.com that looks at something similar - when does the return not outweigh the risk of making certain plays or betting certain levels? It is pretty heavyweight on the maths though and aims to explain the optimum bet levels for certain plays.

Thanks in advance to everyone who sits down with a cup of coffee and reviews the numbers.

This is quite interesting. I have normally thought about AP as maximizing earnings subject to a given ROR. But...it is equally valid to ask the question of how to maximize earnings subject to a given bankroll volatility over time. This is a common concept in securities trading, where individuals frequently give up a (small) portion of return to avoid wild fluctuations in bankroll (and the associated ulcers). Might the same apply to our advantage play?

newb99 is on to something I think. I'm about to head off to work so I can't think deeply about this now, but I did take a quick look at the tables in Appendix A of BJA. For example, Table A52 on page 445, which shows EV for 6D S17: Dealer's Upcard 3. For A,6 v. 3 there are the following EVs:

Stand=-0.113384
Hit=0.030062
Double=0.057996

So hitting instead of doubling gives up ~0.028 EV (a 48% reduction in EV) for the "benefit" of cutting variation from that play in half. Mightn't a player who wants to reduce variation make a few of these plays to smooth out her bankroll curve, while still maintaining an overall positive expectation?




Plays like this would also provide the benefit of some camo.

The purpose of RA indexes is to increase EV with no increase in risk. But, if you simply start making strategy changes to reduce doubling and splitting, this will reduce EV. And if you reduce EV, overall risk will increase. If you are concerned about adding to your initial bet, the solution is to reduce the initial bet (i.e. reduce your unit size), not mess up your strategy.

Why the **** are we even talking about this?! Are you guys completely insane? I get a boner just thinking about doubling down with a max bet against a low card.

Bottom line: under no circumstances should you place a bet so high that you would be unwilling to double down against a 10, muchless a 2-4.

For ****'s sake, learn some risk averse indices, use a smaller unit, or back-count if you want to reduce your variance.

Why the **** are we even talking about this?! . . .

Well . . . . it started with me trying to come up with some figures on what the impact of doing this is. The impact cost if you like. The same as the impact cost of cover plays - wouldn't you want to know the effect of deliberately deviating from BS for whatever reason?

There're many postings on this site surrounding losing bundles despite the high count, and I suspect that the majority of those high count big losses are the result of doubling down against a dealer 2,3,4 - I may be wrong.

For info, in the UK doubling down against a dealer 10 is not a BS play and carries a health warning. And in general, back-counting and wonging in isn't an option due to the fact that at most times tables will be busy, and when they're not you'll stick out like a pair of bulldog's if you do it three or four times (most UK casinos I've visited you can stand on one side and see the other quite clearly - no super Vegas style places here).

So there it is . . . just examining an option for those of us looking to round off the sharp variance edges. If the variance ain't a problem, then it ain't a problem!

. . . You're probably giving up a day's EV by not doubling down a max bet against a 4. It simply should never be done. Period.

Can you quantify that statement with some numbers and the basis for your assumptions please? That's what I was looking for with my original post. I've done some calcs that indicate the loss in EV is nowhere near as high as you suggest, although I'll admit they're rudimentary and need fine tuning at the very least. I do have an open mind on it.