Effect of changing bet spread on expected value

I was told that if you change your bet spread, eg from 5-50 to 10-100, your expected value more than doubles. Can someone explain to me why that is?

In its most common usage, (see the BJ21 glossary) EV (expected value) refers to the percentage you expect to win over the long term.

EV% = 100 x (Long Term Dollars Won / Long Term Dollars Bet)

The related term, EW (expected win) refers to the dollar amount you expect to win during a given period of time (i.e. $/hour).

EW = (EV%/100) x Dollars/Hour bet

EV depends on the casino rules, your count system, your relative bet spread (in your examples you are spreading 1-10), your bet ramp, the cost of camouflage and your error rate. It does not depend on the amount you are betting.

In other words, if you are spreading $5-$50 and decide to double your bet spread to $10-$100, then your EW ($/hour) will also double, but your EV (%) will remain the same.

... I fear there's no real consensus on an EV/EW distinction. You often hear highly respected posters say "My EV for the trip was $250." or some such, and I don't really think the glossary precludes such usage. I think it's best to make everything clear via context. Also, it should be noted neither EV nor EW are generally recognized outside our little bj21 clan, so when writing for the general math crowd, it's best to use "expectation," or "E[parameters]" as per usual.

Alas, the context isn't 100% clear even if you put a % sign after an EV, as in "the expectation for the game is 1.5%," because not all mathematicians will automatically assume you're dividing by the sum of all initial bets, as opposed to the sum of all moneys wagered including doubles and splits. This is just a convention followed in (most of) the blackjack literature; not for all games everywhere.

ETF

Green chip friend of mine told me that if one were to spread from say 5-50 and expect to earn "x" $/hr, that the same person spreading from 10-100 would earn more than 2"x" $/hr. In other words, the EV/hr more than doubles. He asked me if I could figure out why. I can't. Do you know the answer?

If you can avoid the crowded $5 tables, your hands per hour will increase.

Expectation is a linear function. If you double your ramp, your $/hand should exactly double, but $/hr may increase if you can increase hands/hr.

It still may not be advisable for a recreational player to double his ramp. Even with hands/hr held constant, your ROR would more than double to a given bankroll. ROR is not linear.

ETF