If you had 100% on axis, how would you bet?

[Americraps]

My goal is to get as high of a both dice on axis % as possible. Right now, I probably average 46.5%, so I'm a long way off of 100%. But what if you could guarantee 100% on axis? Yeah, I know, you want some of what I'm smoking, but indulge me here. What set would you use, assuming equal on axis distribution, how would you bet and why? I know what I would do, but I want to read what your answers are.

[wudged]

Probably the most obvious is to use the hardways set, bet the hardways all day and hopping, buy/place 4, 6, 8, 10, pass line with max odds.

I imagine you'd be shown the door pretty quickly, though.

Maybe a better strategy would be to bet pass line, establish point on 6/8, bet outside and set for outside numbers (2 4 / 2 5), possibly throw in hard 4/10. Get yourself a few hits then intentionally 7 out.

Or bet strictly the field, mostly using straight 6s but every once in a while switch to 3v. Devise some form of martingale; you will look lucky in never hitting table max / busting out and avoid heat in the process.

Edit:
Completely misread the question. I thought it said 100% PFH (yea, dreamin big!)

[Mad Professor]

Hi Americraps,

In a no-heat/high win-tolerance casino the S-6 (Straight-Sixes) dice-set would probably serve that 100% on-axis shooter the best.

With one each 2 and 12...two each 3's and 11's...one each 4 and 10...two each 6's and 8's...and four 7's; this would give you the strongest on-axis preponderance of high-ratio payouts.

With zero pitch-control, that would produce 6.25% 2's and 12's...12.5% 3's and 11's...6.25% 4's and 10's...12.5% 6's and 8's...and of course 25% 7's.

With an SRR-4 skill-rate, those four Horn-numbers would make for a very compelling advantaged-play.

Anyone want to take a stab at what the player edge would be on the 2, 3, 11, or 12?


MP

[wudged]

Pulling the original formulas from http://wizardofodds.com/games/craps/appendix/1/ and updating them accordingly gives:

2/12:
[(1/16)x30 + (15/16)×(-1)]/1 = 15/16 = 93.75%

3/11:
[(2/16)x15 + (14/16)×(-1)]/1 = 16/16 = 100%

[Americraps]

Wow MP, Wudged! THose are some compelling numbers. I didn't expect to see such a high edge on those horn numbers. I wonder if there are more ways to skin a cat in our fantacy scenario....

[wudged]

Straight sixes would also have hard 4 / hard 10 on axis so you could hop them for the same edge as the straight up 2/12.

I think crossed sixes with a field strategy or iron cross might be best. 12.5% 7 as opposed to the 25% straight sixes has, and still have 2/12 on axis with 8 of the 16 combinations being field-paying. I think a "high edge" and volatile bet such as the field would dissuade the casino from thinking you were up to something.

With a double/double field, you'd have:
((6/16)x1 + (2/16)x2 + (8/16)x-1) = 2/16 = 12.5%

double/triple gives
((6/16)x1 + (1/16)x2 + (3/16)x2 + (8/16)x-1) = 3/16 = 18.75%

[Americraps]

Hmm, I guess I could live with a 12% edge. Any edge is a good one, and Wudge, I like your idea of showing the house that you are just another sucker. After thinking about this for a while, I considered the 3v with an inside bet, I'm sure it would be profitable, but what I would do is set the 2v and bet the four, ten, and PL for the same amount wotco. If you throw a 7 on the co you lose $100 (plus the buy), whereas if you throw a 4 or 10, you win $200, and theres twice as many 4 and 10s than 7s. There are are 4 payers and 2 losers if you keep the dice 100% on axis. The 4 payers pay double. If you have $100 bet on each, assuming equal distribution, you will win $800 (minus the buy ) and you will lose $400, leaving you a $400 profit. Why does this betting scenario sound familiar? OK, I figured that out, now I just have to keep the dice 100% on axis....... Edited to ad- Hop the 52 on every roll

[Maddog]

Reminds me of the old graphs I did that showed on-axis proficency stepping up in 5% incremental improvements. If there is intrest maybe I can did those up again...

From a theoretical point of view and 100% on-axis proficienly I would work with the 100% on-axis theoretical distribution and work my strategy from there.

For reference, here is Heavy’s complete Axial On-Axis Frequency Distribution chart;
[tr] [td][color=Red][b]Axial Set / # Rolled[/color][/b][/td][td][color=darkblue]...2..[/color][/td][td][color=darkblue]...3..[/color][/td][td][color=darkblue]...4..[/color][/td][td][color=darkblue]...5..[/color][/td][td][color=darkblue]...6..[/color][/td][td][color=darkblue]...7..[/color][/td][td][color=darkblue]...8..[/color][/td][td][color=darkblue]...9..[/color][/td][td][color=darkblue]..10..[/color][/td][td][color=darkblue]..11..[/color][/td][td][color=darkblue]..12..[/color][/td] [/tr] [tr] [td][color=darkblue]3-4/3-4 (S6)[/color][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center]0[/center][/td][td][center]2[/center][/td][td][center][color=Red]4[/color][/center][/td][td][center]2[/center][/td][td][center]0[/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td] [/tr] [tr] [td][color=darkblue]5-2/5-2 (P6)[/color][/td][td][center]1[/center][/td][td][center]0[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center][color=Red]4[/color][/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]0[/center][/td][td][center]1[/center][/td] [/tr] [tr] [td][color=darkblue]1-6/1-6 (HW)[/color][/td][td][center]0[/center][/td][td][center]0[/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]3[/center][/td][td][center][color=Red]4[/color][/center][/td][td][center]3[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center]0[/center][/td][td][center]0[/center][/td] [/tr] [tr] [td][color=darkblue]3-4/5-2 (X6)[/color][/td][td][center]1[/center][/td][td][center]1[/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center][color=Red]2[/color][/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center]1[/center][/td][td][center]1[/center][/td] [/tr] [tr] [td][color=darkblue]3-4/6-1 (2V)[/color][/td][td][center]0[/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center][color=Red]2[/color][/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center]0[/center][/td] [/tr] [tr] [td][color=darkblue]1-6/2-5 (3V)[/color][/td][td][center]0[/center][/td][td][center]1[/center][/td][td][center]1[/center][/td][td][center]2[/center][/td][td][center]3[/center][/td][td][center][color=Red]2[/color][/center][/td][td][center]3[/center][/td][td][center]2[/center][/td][td][center]1[/center][/td][td][center]1[/center][/td][td][center]0[/center][/td] [/tr] I'd probably stick with one of the Seven-Avoidance axial set families (3V, 2V, X6) and bet based on the distribution pattern.

Again, from a theoretical stand point my first choice would probably be a 3V set, betting an inside pyramid strategy. My second choice would probably be a X6 set with some type of Umbrella bet.

Even with a 100% on-axis, there is bound to be influence patterns, so I'd be watching what my tossing tendencies show and adjust accordingly.

[memo]

Even with a 100% on-axis, there is bound to be influence patterns, so I'd be watching what my tossing tendencies show and adjust accordingly.

Great point!

Some of the best shooters I have seen have put in untold numbers of practice in order to reach that pinnacle of 50% on axis. Then fight and scratch in order to stay there...Or just above it.

I think the 100% shooter should consider all the thoughts above then spend most of his time trying to figure out a plan that would keep him from being noticed and banned from the casinos.

They would notice and they would communicate to each other. Unlike the blackjack counter, this person creates his own edge at will. I think his time at the tables would be exciting, but once this phonomenel talent was identified, limited shooting opportunities if not out right barring would be close behind.

All that being said...I am not too worried there is any danger.

Memo

[Maddog]

...Some of the best shooters I have seen have put in untold numbers of practice in order to reach that pinnacle of 50% on axis...

This is a good point Memo, though I'm not sure I would characterize 50% as the "Pinnacle", but more like the DI target on-axis percentage.

When I'm really on my game my on-axis % hovers around the 50-52% range. I think you need to be at least 48-49% to feel like you are getting consistency in your table results. Anything less then that and you can certainly still have winning sessions, but the variance takes a greater toll on you mentally.

[memo]

[quote="Maddog When I'm really on my game my on-axis % hovers around the 50-52% range. I think you need to be at least 48-49% to feel like you are getting consistency in your table results. Anything less then that and you can certainly still have winning sessions, but the variance takes a greater toll on you mentally.[/quote]

Now that is some information that one can really use...
Yes, pinnacle may not have been the correct word..But in another sense, so few of us ever really get there. It still applies.

I work to stay over 48% with some consistantly. Sometimes peaking a bit higher.
Any thoughts about how hard it is to get from 46 to 48% then, difficulty in getting to 49%, 49.5%...50% etc. And staying there with any consistancy...?
Honeymoon is over..Reality is kicking in.

Memo

[Maddog]

Right, Memo, it's the probability stuff. Every percentage point you move the needle away from the median of on-axis improvement is more difficult then the last.

I once described it as being like poor Sisyphus pushing his rock up the hill. Each step more difficult then the last and the unrelenting gravity of expected probability (or inundation of results) working to pull the rock back down to the bottom (standard median).

If one were to image a standard distribution bell curve, we know that probability tells us that any one instance/event can show up anywhere on that bell curve. Just like any one crap hand can be ultra short, or ultra long, or anywhere in between. But probability also tells us that when we take a large enough collection of those single hands, we will find that the majority of them will turn out to be found around the median.

In my mind, I've always thought of DI as a means to "adjust" the position of that median. And the trick is being able to determine the difference between a true and consistent alteration of the median versus a case of expected variance within the sample.

It should be encouraging to understand that the further one gets from a random expectation of 44% on-axis the harder it is to stay there, and accomplishing it consistently over time is a great achievement.

Here is another way to think about the situation:

Assume we have 48% on-axis shooting, meaning we have 52% off-axis shooting, and for argument sake assume that the 52% off-axis are simply random results (which for most people they basically are).

What you have is 52% of your results showing the expected standard distribution of six 7's, five 6's&8's, four 5's&9's.. etc. And you have 48% of your results showing the 16 possible outcomes of your chosen axial sets distribution. Combine the two result groups together and you might see that what is happening is your on-axis results are BOOSTING your off-axis standard distribution results.

When you look at it that way, I think you see that off-axis results are nothing to be overly upset about and that improving your on-axis results as much as possible is something highly desirable to achieve.

[Blackcloud]

UNHH!!If always on axis, BC would be committing a crime with Kamikaze come-out

[memo]

Assume we have 48% on-axis shooting, meaning we have 52% off-axis shooting, and for argument sake assume that the 52% off-axis are simply random results (which for most people they basically are).

What you have is 52% of your results showing the expected standard distribution of six 7's, five 6's&8's, four 5's&9's.. etc. And you have 48% of your results showing the 16 possible outcomes of your chosen axial sets distribution. Combine the two result groups together and you might see that what is happening is your on-axis results are BOOSTING your off-axis standard distribution results.

When you look at it that way, I think you see that off-axis results are nothing to be overly upset about and that improving your on-axis results as much as possible is something highly desirable to achieve.

Don't you think though, that our tendancy to repeat things...
Our consistancy to do the same thing, may move in some way to the off axis results, giving in a small way a sort of influence, even though that is not exactly what we are trying to achive?? ie. When I go on a horn jag...Some are on axis, some are not, but they seem to group up.

I am thinking that even our off axis results may have some influence.

Memo

[Maddog]

...Don't you think though, that our tendancy to repeat things...Our consistancy to do the same thing, may move in some way to the off axis results, giving in a small way a sort of influence, even though that is not exactly what we are trying to achive?...

Yes, absolutely. Influence of on-axis results is not mutually exclusive to influence of off-axis results. Theoretically the consistency of the toss mechanics that result in on-axis can transfer into patterns of specific off-axis behaviors.

I believe the off-axis influence is a by-product of the efforts of executing a consistently repeatable controlled toss. But the value in efficacy of the on-axis results will far outweigh what is provided by the off-axis pattern.

[realtime]

Just like any one crap hand can be ultra short, or ultra long, or anywhere in between. But probability also tells us that when we take a large enough collection of those single hands, we will find that the majority of them will turn out to be found around the median.

In my mind, I've always thought of DI as a means to "adjust" the position of that median. And the trick is being able to determine the difference between a true and consistent alteration of the median versus a case of expected variance within the sample.

Maddog,

Believe me I will never claim to be a math/statistics whiz, but what you stated about the median length of hands to me is probably the most important fact to know about my hands or anyone I want to bet on. Speaking in laymans terms, if I know that I/they more often than not generally get X throws in before the hand ends and my/their throw is "up to par" that session, I pretty much can develop a betting strategy that will be a winner for that session knowing that once X throws have passed danger lurks.

My question to you is why is so much emphasis put on SRR instead of "the median" issue which seems much more useful than the "average" length of a hand the SRR represents? Shouldn't we be talking more about and calculating this median length of hands to bet the most efficient way based on each persons skills?

Mike

[Maddog]

realtime,

Basically "Average Hand Length", "SRR", and "Median" are used synonymously. Each has a slightly different specific meaning, but in layman's terms at the craps table they are all close enough to be equivalent.

When we talk about Median (or more correctly the Mean) we talking about some form of average. With craps this is most often associated with hand-length... but it could be anything.. like number of eights in a hand, or number of inside numbers before a seven, etc.

Where all this theoretical stuff really screws with us craps players is when you get involved with a hand like the one we see going in Heavy's simulated craps game on the other thread. That hand has nothing to do with means or averages, and everything to do with betting discipline and philosophy. Most people are courageously sticking to their betting plan, even with all the comments we hear about "taking what the table gives you", heh heh heh.

[Bick]

I've been working on my toss now going on four years, and am always wondering what defines
the upper echelon of DI's regarding SRR, on-axis %, primary face hits, etc. Not like golf or bowling,
where you can check out a fellow players handicapp. So this thread has given me some perspective
when I see comments regarding getting from 44 to 46 % on-axis vs moving into the 48% range, and then the added difficulty of moving up to 49-50+. It sounds like golf. Anybody can get their handicapp
down from 30 to 20. Takes a little work though to get from 20 to 10. I was at 8 for twenty years and
decided to see what it takes to get to scratch. After practically living at the course for two years I
could do no better than 3. Then I started to build my own house, then two kids appeared from somewhere, and I haven't played a round of golf in 12 years. Craps is much more fun.

Bick

[heavy]

Then I started to build my own house, then two kids appeared from somewhere, and I haven't played a round of golf in 12 years. Craps is much more fun.

You'll always hear comparisons of DI to golf, and I tend to agree. However, I can dust off the dice after a three month lay-off and be tuned up pretty good in 4 - 5 days. After 30 + years of trying to hit the golf ball I still can't fade the ball when I want to. Making those kids appear from somewhere is much more fun.

[heavy]

Everything else being okay - ball goes in direction that face of club is pointing -

Yeah, but even Tiger Woods can't get that down right. How is a duffer who plays golf half-a-dozen times a year and never practices supposed to develop any consistency? Ah. Right. Same way the dice guys who never practice and rarely play do. Not very well.