ROR and Penetration

I purchased the AOII version of BJA3 ch10 and I am amazed at the effect of penetration on Risk of Ruin - eg:

1-12 spread H17DAS

----------400 unit bank -- 800 unit bank
5.0/6 ----29.6%---- -------8.8%
5.5/6 ----19.9%---- -------4.0%


Oh my gosh, I want to keep my ROR in the low single digits!

Perhaps it's better for me to travel to better games and attack them harder rather than gnaw away at local games with worse penetration...

I always thought that a high TC was a high TC no matter what..

Can someone explain why an increase in penetration has such a marked effect on lowering ROR?

And how does this also decrease the N0 and make the "long run" easier to reach?

It's not the pen that is lowering your ROR, it's the fact your bankroll doubled. (.296*.296=.088 etc)
Double your $ roll and your lifetime ROR will be former ROR squared. (.199*.199=.04)
Is that what you mean?

Doubling,tripling, halving your roll will have no effect on the number of hands to reach N0. Any roll will neither increase nor decrease the number of hands to reach N0. Assuming same $spread.

The more roll you have, the more likely you will be able last long enough to play that many hands and achieve it. That's all.

The deeper pen - the more we know about the remaining cards and our advantage and or disadvantage. And the more we know - our bets reflect this and are more accurate. Thus, reducing our RoR.

Thanks for that formula on BR, but I guess I'm more interested in the 5.5/6 4.0% changing to 8.8% at 5.0/6 - having the dealer move the cut card forward 26 cards more than DOUBLES my ROR?!

I believe it. But I don't think there are many (any?) legit places left with consistent 5.5/6.

Because your advantage is increasing more than your variance. RoR is essentially a comparison of EV to SD. When your SD (relative to your EV) is low you are not taking much risk to reach your reward. Less risk means less of a chance of going broke. Deeper penetration increases your EV but your SD doesn’t change much. Look at the charts and see how those two numbers change as the penetration changes.

Same reason. N0 is also a comparison of EV to SD. A lower SD means smaller bankroll swings. Since the bankroll swings will be smaller you will be able to overcome them and approach your long-run expectations sooner. The game is less volatile so you are less likely to be far away from your EV.

It all depends on how you play it. If the game allows surrender then your EV will increase and your SD will decrease – the perfect situation! Spreading to multiple hands can have the same effect. Sometimes a small change in EV and/or SD can have a significant effect on your RoR and N0.

-Sonny-

OK - I think I see what you mean now. I may have been thrown off by the fact you specified equal unit rolls.

It's like Sonny says, obviously the better pen makes for a better game. Better ratio of EV to SD.

First, remember with the same total $roll, one can always bet in a way to keep one's risk the same.

Take your 2 games with a $10K roll. In a 5/6 game maybe you play-all and spread 1-12. In order to "optimally" bet, in order to maximize that EV to SD ratio, maybe that means spreading $10-$120. You have a 1000 unit roll with $10K.

In the 5.5/6 game, optimally spreading the same 1-12, might mean you now spread $15-$180 with the same $10roll. Your ROR will be about the same in that case but in the 5.5/6 game it's a 667 unit roll. Your unit rolls are not equal.

Bet $15-$120 in the 5/6 game as you did in the 5.5/6 game so you keep it the same 667 units in either game and your ROR will actually be higher in the 5/6 game than the 5.5/6 game since you needed 1000 units before to keep your risk the same but now only have 667 units.

Bet $10-$120 in the 5.5/6 your ROR will go down compared to the 5/6 game because you now have a 1000 unit roll, the same as you did in the 5/6 game except you only needed 667 units to play with the same risk. You now have more units in same $roll if you bet that way when and if the game changes back to 5/6 because you only needed a 667 unit roll to keep your risk the same.

Not to mention that the points at which one spreads 1-12 will be a different number of units at various TC's. Preobably doesn't make a huge difference lol.

A better game means you can maybe bet the same $roll with a different $min unit but same 1-x spread.

It's a little confusing I know. My point is if you liked the 8% ROR in the 5/6 game, then bet in such a way that will create about the same 8% ROR in the 5.5/6 game. Or, if you like the 4% ROR of the 5.5/6 bet in such a way that you will have the same ROR in the 5/6 game.

Either change your $unit size with the same $roll to make this happen or increase your total $roll and keep $unit size the same to make keeping risks identical.

Bet optimally with the same risk and 1-x spread and same $roll, you will have higher $EV in the better game.

You can't have same total $units with same $roll in both games and expect to keep risk the same.

"Better" games don't magically decrease ROR. It depends how and when and how many $'s you choose to bet at the various TC's since you will get higher frequencies of TC's in "better" games.

If you choose to bet only $10-$120 in the 5.5/6 when you could bet $15-$120 with the same risk and same $roll, not to mention increased EV both absolutely and relative to SD when/if you did, why wouldn't you?

By way of example, here's my sheet for Tables 10.60 and 10.61 from Don's book for a 1-12 spread. Fool around with the stuff in red to satisfy your curiosity - chnage $rolls, unit spreads, $units as you want. The first 2 groups are just for comparison and are the 1-12 spreads from his tables with a $10K roll. The second 2 tables (columns M thru W) are for you to change unit spreads, $unit, $roll etc for comparison and have fun with and see what changes.

Hopefully, just by way of example, food for thought anyway lol.

If I can try to answer any questions, let me know.

Ultimately, buy a sim, and run what you want lol. That's the ultimate answer.

Forgot to attach the sheet lol.

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