If you don’t already know how being able to successfully repeat just one-half (50%) of your PL-Points can double and then keep re-doubling your gaming bankroll; let me show you again.
The Basics of How & Why
~Let's say a shooter throws just as many Point-Cycle winners as he does Point-Cycle losers. That means he’ll repeat his PL-Point 50% of the time and he’ll 7-Out before repeating his PL-Point about 50% of the time too.
~Let’s also say that this 50% PL-winners/50% PL-losers shooter starts out with $10 bets on the Passline and backs it with an average of $40 in Odds in a 3x/4x/5x-Odds casino.
~That means a PL-Point repeater will pay an average of $70 when it wins ($10 in flat-bet even-money payout from his PL-wager, and an average of $60 in Odds profit). It also means that he’ll lose $50 when he fails to repeat his PL-Point.
~On average then, he’ll produce a net-profit of $20 more when he wins than when he loses. In case you’re keeping track of such things; that is a 20% return on investment (or 10% ROI per wagered hand) for this 50/50 shooter (he invests/wagers a total of $100 over each of two hands, and he produces a net-profit of $20), even though he is only winning one-half of his bets.
~At a 20% return on investment; it would theoretically take him an average of just five (5) hands before he doubled the money required to double his base-bet from $10 on the Passline with full 3x/4x/5x-Odds. However, here in the real-world, there would be quite a bit of back-and forth winning-and-losing variance built into his hand-to-hand outcomes, and that is what we’ll be looking at today.
For a much fuller exploration of this 50% PL-Point Win-Rate subject and how you can use it to double and then keep redoubling your gaming-bankroll; I would invite you to read my “Will Winning 50% of Your PL-Points Make You Rich…Stinking Rich…or Obscenely Wealthy?” article.
Understanding Why PL-Odds Can Grow Your Bankroll at an Unparalleled Rate
Let’s review the three most important verities of dice-influencing advantage-play:
~The higher your PL-Odds…the more your dice-influencing skills are leveraged in your favor.
~The higher your PL-Odds…the fewer times you’ll have to throw a PL-Point repeater in order to recover (to break-even) from a previous PL-Point loss.
~The higher your PL-Odds…the quicker your dice-influenced outcomes will double and then keep re-doubling your bankroll.
Let’s first consider how the higher your PL-Odds are, the fewer times you’ll have to throw a PL-Point repeater in order to recover a previous Point-then-7-Out loss.
Now let’s take a look at how PL-Odds affect your advantage when you know what your PL-Point win-rate is. In this case, we’re talking about a player who wins half of his PL-Points, and loses the other half.
Understanding Hand-to-Hand Variance
Even though this shooter has a 50% PL-Point win-rate, his skills aren’t going to gloriously manifest themselves on each and every hand. We have to expect some hand-to-hand and session-to-session variance. That’s just the nature of the beast we call advantage-play dice-influencing.
We are looking to the overall effect that our skilled shooting produces. We know that if we take a big-picture view of our overall talents, and we bet them accordingly (instead of trying to zig and zag all over the place based on whatever arbitrary outcome that you just tossed); then your skills will prevail and they will do so in profitable ways that you never thought possible.
How Odds Determine Bankroll-Growth
~While we can probably safely say that this shooter using 1x-Odds would need in the neighborhood of 32 hands in order to get enough money to increase his base Passline wager from $10 to $20 while sticking with 1x-Odds; while the same shooter using 2x-Odds would possibly only need around 20 hands to do the same thing (though 25 hands is more in the realm of probability); we have to account for a little more variance as we climb the Odds-ratio ladder.
~For example, while it could theoretically only take this shooter about 10 to 12 hands to move up his base bets (while sticking with 3x/4x/5x-Odds); I think it is more reasonable to assume it would take in the neighborhood of 20 hands to do so. Likewise, I think it would be reasonable to project that it will probably take him nearly just as long while using full 5x-Odds on all of his PL-Points.
~Similarly, even though this shooter’s blended-edge rises dramatically when using 10x-Odds to back his PL-Points; it could take around 18 hands for his bet-wins to outpace his bet-losses (on these 50/50 PL-Point w/Odds wagers) before he could reasonably increase the base-value of his Passline wagers.
~Likewise, the same pretty much holds true when he is using 20x-Odds under a similar 50/50 win/loss scenario. It would probably take around 17 hands for him to achieve his goals.
Trying to CONTROL Variance is a Fool’s Errand
Even though we have a good handle on the approximate number of hands he’ll likely have to throw in order to feel like his bankroll is growing at an adequate rate and doubling ‘on schedule’; how much actual hand-to-hand variance should he honestly expect to encounter along the way, and how streaky will some of his sessions be?
Ahhh, now there’s the question that keeps many talented dice-influencers under-betting their own proven advantage, while sticking with less-optimal, but more-comfortable disadvantaged wagers.
In other words, many players would rather stick with negative-expectation wagers where they are comfortable in knowing what their approximate loss-rate will be; rather than to switch to positive-expectation wagers where the fear of unknown-but-anticipated volatility and hand-to-hand variance-swings may see deeper bankroll draw-downs than they are currently used to, but which are a natural occurence on the way to much greater overall profits that far exceed anything that they can currently even imagine.
That is, they spend all their time foolishly trying to ‘protect’ their bankroll (by sticking with neg-ex or low-edge/hedged/or under-funded pos-ex wagers where they know they are pretty much bound to lose or stay close to even); but at a loss-rate or break-even rate that they have become quite comfortable with; instead of putting their bankroll to better use on adequately-sized, higher proven-advantage non-hedged pos-ex wagers, but where the deployment of that betting-capital will mean quite a bit more back-and-forth bankroll variance on the A-P journey to doubling and re-doubling of their money again and again.
Trying to CONTROL variance is a fool’s errand that will see you wasting all of your time making under-optimized bets that are aimed at ‘protecting’ your bankroll, while leaving little to no room for actual overall bankroll-growth.
When you ask yourself why your bankroll isn’t growing anywhere near as fast as it should be, despite your validated D-I talents; the answer invariably comes back to how you use your money when you are in the casino.
Today, we can answer that variance question to a high degree of confidence; and perhaps in doing so, help to move at least a couple of our community’s 50% PL-Point win-rate shooters one step closer to doubling and re-doubling their bankroll at a rate that is more in keeping with what their D-I talents really deserve.
How Much Streaky VARIANCE Should We Expect Along the Way?
In the case of our 50% PL-Point win-rate shooter; it’s pretty easy to figure out.
Since we know that he will average one winning PL-Point for every losing one; it is quite likely that he’ll experience the following streaky variance along the way:
~2 losers in a row for every 4 hands
~3 losers in a row for every 8 hands
~4 losers in a row every 16 hands
~5 losers in a row every 32 hands
~6 losers in a row every 64 hands
~7 losers in a row every 128 hands
In Part Two, we’ll look at what effect that kind of streaky variance can have on his bankroll, and what kind of draw-downs he should fully expect to endure along the way to doubling and redoubling his money.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
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