Is There Unknown Value in Certain Types of Bets?
As dice-influencers, are we prone to overlook certain betting-opportunities because of what we THINK we know about them?
If you were to ask a group of D-I advantage-players to rate the risk/return ratio of various multi-number global-bets like Inside, Across, Outside, Even and the Iron Cross; most would probably rate the Inside-bet as offering the best return-on-investment, while the Iron Cross would mostly be burdened with the title of worst among the lot.
If you consider any of the global-bets in the traditional context of return-on-investment per paying hit; then it’s easy to see why some multi-number bets are held in far higher esteem than others.
Take a look:
Inside-bet Includes Place-bets on the 5, 6, 8, and 9
Basic cost: $22.00
Weighted Payout/hit: $7.00
Per-Hit Return-on-Investment 31.8%
Across-bet Includes Place-bets on the 4, 5, 6, 8, 9, and 10
Basic cost: $32.00
Weighted Payout/hit: $7.50
Per-Hit Return-on-Investment 23.4%
Outside-bet Includes Place-bets on the 4, 5, 9, and 10
Basic cost: $20.00
Weighted Payout/hit: $7.86
Per-Hit Return-on-Investment 39.3%
Includes Place-bets on the 4, 6, 8, and 10
Basic cost: $22.00
Weighted Payout/hit: $7.75
Per-Hit Return-on-Investment 35.2%
Iron-Cross (Anything but 7)
Includes Place-bets on the 5, 6, and 8, plus a Field-bet
Basic cost: $22.00
Weighted Payout/hit: $4.10
Per-Hit Return-on-Investment 18.6%
So, when appraised from a traditional return-on-investment-per-hit point of view; these global-bets are ranked as follows:
Outside 39.3% Even-Number 35.2% Inside 31.8% Across 23.4% Iron-Cross 18.6%
But is that the real story and is per-hit R.O.I. the best indicator of their potential in the hands of a dice-influencer?
Are we seeing the full potential of each of those bets, and is there possibly any latent attributes that are hiding within the seemingly lackluster performance of global-bets like the Iron-Cross or All-Across wager?
I think there is.
One of the metrics that dice-influencers use to measure success is their Sevens-to-Rolls Ratio (SRR), which represents your ability to alter the ratio between 7’s and non-7 outcomes. Our SRR also tells us how long, on average, our Point-cycle will generally last before we 7-Out.
So an SRR-7 means that our point-cycle will generally last for an average of seven rolls before the 7-Out ends it; and a Sevens-to-Roll Ratio of 1:8 means that our point-cycle will usually last an average of eight rolls.
Another metric that savvy dicesetter’s use to figure out how many paying-hits their wagers will generally enjoy before they throw a roll-ending 7-Out is the expected hits-per-hand for a given bet-type.
This is where things get real interesting.
As your SRR-rate increases and the number of 7’s that you throw decreases; the non-7’s that replace those reduced-appearance 7’s is where the bulk of your advantage over the house comes from.
In my Regression Avoids Depression series, I’ve codified precisely how the per-roll probability-rate for a given bet changes in lock-step with the SRR.
There are some excellent pieces of roll-tracking and edge-determining software out there. Maddog’s BoneTracker v5.0 is one that I heartily endorse, not only because DiceTool has now been fully integrated into it; but more importantly, because it shows you the exact hit-rate ratio at which you are currently throwing most of the global-bets that we’re talking about today. So obviously you can and should use that percentage to determine exactly where your multi-number global bet stands in relation to it’s true return-on-investment over your entire point-cycle duration instead of just on a per-roll basis.
But even without software like that, it is important to understand that your per-hit return-on-investment is not the be-all and end-all of sustainable money-making. Rather, you also have to look at how frequently your chosen wagers are likely to hit during a given average point-cycle and figure out if the total rate-of-return is to your satisfaction or whether a better skill-matched-to-advantage betting-regimen is called for.
When you factor your expected point-cycle hit-rate for these global-bets against their weighted payouts; you gain a whole new perspective and perhaps even a whole new respect for some of the global-type bets that have long been looked down upon.
Let me show you what I mean.
Expected overall hit-rate:
Inside 50.0% Across 66.6% Outside 38.9% Even-Number 44.4% Iron-Cross 83.3%
When we know a players SRR-rate, we know how long his average point-cycle will last, so we can immediately determine how efficient each one of these global-bets are. That is, we can determine how well each of these global-bets utilizes each roll within a players point-cycle.
When we do that, the resultant overall expected hit-rate/point-cycle offers a glimpse at what may be some otherwise overlooked potential. Take a look:
Inside 18 outcomes out of 30 non-7’s = 60.0% p-c hit rate
Across 24 outcomes out of 30 non-7’s = 80.0% p-c hit rate
Outside 14 outcomes out of 30 non-7’s = 46.7% p-c hit rate
Even 16 outcomes out of 30 non-7’s = 53.3% p-c hit rate
Iron-Cross 30 outcomes out of 30 non-7’s = 100.0% p-c hit rate
If we take a players point-cycle SRR and multiply it by these hit-rate figures, we can determine how many times you are likely to hit each of these global-bets during your point-cycle and therefore determine how net-profitable each multi-number bet is likely to be.
In other words, if you really want to test the efficiency of your bets, you not only have to look at their return-on-investment on a per-hit basis; but you have to consider their total overall return-on-investment over the entire expected duration of your point-cycle.
Now admittedly this is a simplification to illustrate how rate-of-return when measured on a per-hit basis does not tell the whole advantage-play story, and obviously you’ll be best served by using the above-noted software to verify your particular edge; but the following example illustrates my point quite nicely.
When you multiply a given SRR-rate by the expected point-cycle hit-rate you determine how many paying hits each SRR is expected to generate during its average point-cycle.
SRR-7 Hits-per-PC Gross Rev/Net-Profit ROI/hand
Inside 4.2 $29.40 $7.40 33.6%
Across 5.6 $42.00 $10.00 31.3%
Outside 3.3 $25.94 $5.94 29.7%
Even 3.7 $28.68 $6.68 30.4%
Iron-Cross 7.0 $28.70 $6.70 30.5%
SRR-8 Hits-per-PC Gross Rev/Net-Profit ROI/hand
Inside 4.8 $33.60 $11.60 52.7%
Across 6.4 $48.00 $16.00 50.0%
Outside 3.7 $29.08 $9.08 45.4%
Even 4.3 $33.32 $11.32 51.5%
Iron-Cross 8.0 $32.80 $10.80 49.1%
SRR-9 Hits-per-PC Gross Rev/Net-Profit ROI/hand
Inside 5.4 $37.80 $15.80 71.8%
Across 7.2 $54.00 $22.00 68.8%
Outside 4.2 $33.01 $13.01 65.1%
Even 4.8 $37.20 $15.20 69.1%
Iron-Cross 9.0 $36.90 $14.90 67.7%
When you look at each of these global-bets with an open-minded perspective, the bets that most people ‘perceive’ to be sub-par when compared to the more-accepted traditional multi-number wagers; you'll find that some are in fact not only in the same league, but they’re also pretty much on par with their more time-honored and revered brethren.
So, Is There Unknown Value in Certain Types of Bets?
That’s entirely up to you to decide, but it seems to me that some of them aren’t quite as ‘ugly’ as they’ve been portrayed as being by some fellow players who really should know better.
When it comes to rejecting certain betting-methods out of hand; you may want to look a little deeper than to blindly accept what you’ve always been taught to believe.
Good Luck & Good Skill at the Tables…and in Life.
The Mad Professor
Copyright © 2006