In order to illustrate and isolate the effects of different strategies on variance and skew, I wrote a program to simulate the play of five different players, all experiencing the same series of outcomes, for 40,000 sessions of 60 passline bets each (or until some other stop condition took place). I ran three sets of these, the first with just passline bets, the second taking double odds and third taking 3, 4, 5X odds. I used the same RNG seed for each set of sessions.

The five players had these characteristics:

1. constant $5 bet amount, no stop conditions other than 60 bets
2. constant $5 bet amount, but with a stop condition of a loss amount
3. constant $5 bet amount, but with a stop condition of a win amount
4. 50% progression after every win, no stop condition
5. 50% progression after every loss, no stop condition

I didn’t combine any of the characteristics, in order to isolate their effects. Later, I will simulate some combinations.

First, for the passline without odds, for which the theoretical figures are:
60 bets: ev -$4.24, SD $38.73

The graph for Guy #1 is the familiar bell-shaped curve. With a stop-loss of $50, you cut off the left tail and build a spike at -$50, with the opposite effect for a win-goal stop condition, except the spike is smaller. It’s easier to lose $50 than win it. The progressions really kick in the “skew”, as progressing on a win results in lots more losing sessions but large wins when the dice cooperate, a “right skew”. Progressing on a loss creates more-or-less of a mirror image of progressing on a win, a “left skew”. Naturally, since these “guys” were betting more, their mean loss is larger. When you’re not taking odds, to get variance you have to progress your bets.

Now, for $5 passline (base bet), taking double odds, stop-loss and win goal each $100
60 bets: ev -$4.24, SD $110.67

First, notice the effects of taking odds on all the “guys”: about the same mean outcome, but lots higher SD, more winning sessions, larger wins and larger losses. No surprises. Even doubling the stop-loss and win goal, more shortened sessions for Guys #2 and #3. Of the 40,000 sessions, Guy #4 had 392 wins of over $1000, 18 of over $5000. Guy #5 had 36 sessions losing at least $5000, 503 losing at least $1000. Of course, those are still very low percentages of all the sessions.

Comparing the different strategies in the double-odds scenario, we see pretty much the same relationships as we saw without odds, somewhat less variance for Guys #2 and #3, lots more for #4 and #5, more winning sessions for #3 and #5, more losing sessions for #2 and #4.

(Notice that the stop-loss and win-goal can be “overshot” by a bit when you’re taking odds.)

Now, for $5 passline (base bet), taking 3, 4, 5X odds, stop-loss and win goal each $150
60 bets: ev -$4.24, SD $190.37

Kicking the odds up for Guys #2 and #3, even with $150 as the cutoffs, still results in more shortened sessions. Guy #5 has 15 sessions winning over $10,000, 59 winning over $5000 and 1064 winning over $1000. Still, the odds are about 37-to-1 against winning $1000 or more. Guy #5 has 1261 sessions losing at least $1000, 83 losing at least $5000 and 26 losing $10,000.

If I had kept the magnitudes of the stop-loss and win-goal constant, the number of shortened sessions would have been much greater, of course.

Next, I will combine some of these strategies, giving Guys #4 and #5 a stop-loss, a win goal, and maybe both.
Cheers,
Alan Shank

Good stuff!

Great post Alan, looking forward to your next one. If you get the time, it’d be good to see data for 10x odds as well.

Jacob - 20 April 2010 12:59 PM

Great post Alan, looking forward to your next one. If you get the time, it’d be good to see data for 10x odds as well.

Thanks.

You know, I ran into a problem when running the Guy #4 with a $150 stop-loss and 3, 4, 5X odds. One of the sessions ended up down $1466, so I thought there was some program error, but there wasn’t. Here’s what happened:

There were 11 wins in a row, and Guy #4 increases bets 50% after each win, so the flat bets went
5 7 10 15 22 33 49 73 109 163 244 366

At that point, Guy #4 was up $730, but the point was six, so the odds bet was $1830, for a total of $2196. The bet lost, resulting in a net loss of $1466. Well, I don’t know if you could even bet that much on the odds, but presumably you wouldn’t if you only were willing to lose $150. I need to put in some code to prevent bets that would, if lost, put the player below the loss limit. Of course, $150 is not a very realistic stop-loss for that aggressive a player, anyway.

I might just modify the whole Guy #4 so that the odds increase from double up to, as you suggest, 10X, before the base bet goes up. That is more in line with my principle of maximizing the amount bet on the odds. I might do that for Guy #4, who progresses after a loss, too.

So, it will be a week or two before I post the next set of results, because I have a busy week and am attending a reunion in Fresno over the weekend.

Still can’t preview the post, I see.
Cheers,
Alan Shank

goatcabin - 20 April 2010 01:51 PM

Jacob - 20 April 2010 12:59 PM

Guy #4 was up $730, but the point was six, so the odds bet was $1830, for a total of $2196. The bet lost, resulting in a net loss of $1466.

The math work is fascinating. Watching the dealers and box calculating the payoffs would be one of the great sights of our time.

Ditto on the lack of preview (at least in Firefox).

Yeah, I know the previews are still broken. ExpressionEngine still hasn’t released a fix for this bug, and it isn’t the sort of thing I can fix on my own. I’ll head over to their site right now and try and get a hold of the devs to see if they have made any progress on a fix.

In the mean time, previews are working on http://www.smartergamblers.com/forum so if you have a lot of formatting work to do, you can use the preview functionality over there, then copy and paste to crapsforum once you are happy with it. Obviously not ideal, but perhaps it may be of use to you.

Jacob - 20 April 2010 02:40 PM

Yeah, I know the previews are still broken.  ...  In the mean time, previews are working on http://www.smartergamblers.com/forum so if you have a lot of formatting work to do, you can use the preview functionality over there, then copy and paste to crapsforum once you are happy with it. Obviously not ideal, but perhaps it may be of use to you.

Since I have the ability to edit my own posts I just submit, then try again if it doesn’t look the way I want it to.  I suppose someone could get a draft copy if site usage were heavy, but I don’t consider that a big problem.