And as pointed out in the article, these particular values of a and b, and the computation of any intermediate values v, all depend on the particular game being studied: the number of decks, rule variations, penetration, etc.

Also, as you point out, everything presented here focuses on playing (vs. betting) strategy, essentially assuming flat betting throughout. To evaluate the effect of betting strategy, we need to be able to efficiently (and still *exactly*) compute not just the expected return, but the entire probability distribution (or at least the variance) of outcomes of a round. This required some significant new algorithm development, which is described in another later series of posts here, here, and the punch line with win rates and RoRs for various index strategies here.

]]>How did you cone to the figure of -0.001906 from -0.2333%.

The scattergram images are showing the effects of flat bet strategy? If so a spread of x12 at TC5 will have an even greater effect from index plays? ]]>

For example, consider the P(Passenger total weight > 35000) in both distributions. Assuming I did not make a mistake, it is roughly .25% for the 175 passenger plane and only .03% for the 173 passenger plane.

Likewise for P(Weight>36000), we have roughly 1 in 200,000 for the 175 passenger plane and ~1 in 5,000,000 for the 173 passenger plane.

]]>Brent Pella – Why You Shouldn’t Fly on Spirit Airlines ]]>

With CDP, on the other hand, you don’t have to *always* double down; instead, you can vary strategy depending on *how many* hands are split. This is arguably the least realistic setting (it’s really only included since it’s easily computed), since the cards aren’t dealt this way in practice: you would have to split *and re-split* repeatedly, *then* go back and play each resulting hand to its completion.

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