[MentalNomad]

DavidC, I don't know how much you know about BJ. . . your reasoning is pretty much on target, but you're missing a piece of the picture.

Playing BJ line, you're playing to a disadvantage. The bonus dollars, however, are bigger than the disadvantage. The game, therefore, is to wager only enough dollars to clear the bonus.

If it takes $1000 of action to clear a bonus, and the game rules results in a 1% disadvantage, you expect to lose $10 while clearing the bonus (on average.)

If you wagered $0.10 a hand enough times to make $1000 in action, you are likely to lose somewhere around $10 when all is said and done.

If you wagered $100 per hand 100 times, you still have the same expectged $10 loss. . . but the variance will be so huge that you could tap out a $1000 very, very easily.

When you bust out and cannot complete the bonus, not only do you bust out, but you also don't get the bonus. Busting out is a travesty because you still have time played at a disadvantage.

All that having been said, in terms of time efficiency, the best way to clear bonus is to play the highest bets you can afford. If you had an enormous bankroll, you could just bet $1000 once and be done with it. Your expectation will be the same in the long term, because you'll do it every month, and the time invested will be small. But you would need a CRAZY bankroll to do that.

If you are forced to work within a bankroll limit, you need to size your bets to avoid busting out. Remember, playing is not profitable, and busting out kills all profit potential.

The smaller the bet increment, the more certain your loss rate, and therefore the more likely you are to survive to clear bonus. But, as you say, the smaller the increment, the lower your effective hourly earnings. That's the balancing act.

To maximize growth rate of a bankroll while minimizing the risk of busting out, you might try to use Kelly Criterion betting -- when you play to an advantage of, say, 1%, KC states that it is ideal to bet 1% of your bankroll on each wager. If you have losses, your bet shrinks, avoiding the bustout. If you have wins, your bet increases, taking advantage of the bigger bankroll immediately. The KC maximizes your growth rate.

The trouble is, the BJ online plays to a DISADVANTAGE. The proper amount to bet is not to bet.

The KC calculation doesn't apply well to the bonus, because the bonus is not a wager. It's a guaranteed payout. But you might still try to use the mathematical experience we gain from Kelly Criterion analysis and apply it here.

Say you choose an initial bet size which offers a good balance of $$/hour for your personal preference. . . and make sure you have the bankroll to support it. Say you need to clear the $1000 of action, you have a $200 bankroll. You might start with a $10 bet size, or 5% of bankroll. If you get lucky and get ahead to $300, you then bet $15 per hand. This will speed up your play-through for the bonus, and increases your effective hourly profit. If you are unlucky and the bankroll drops to $100, you will be betting $5. By cutting the bet, you prevent yourself from losing the remainder to an unlucky streak. Of course, you'll have to play a lot more hands at the smaller bet size to clear the bonus, but again, that's a guaranteed payout -- time is the only issue.

Ideally, you would scale the bet in smaller increments. So if you went from $200 to $220, you would move your bet from $10 to $11, or if you dropped to $180, you would bet $9.

The results would be that some sessions would be very short, because you went on a tear, increased your bets, and cleared the bonus quickly. Other sessions would be very long, because you had a crappy start, cut your bet size to a tiny amount, and had to grind it out.

The irony: in the long term, the shorter sessions will balance the longer sessions, and I suspect (no mathematical proof here, but assume a 50/50 game here) that the average amount of time needed will be the same as if you had just kept betting $10!

So why not just bet $10 always? Because you would need a bankroll much bigger than $200 to guarantee you clear the bonus.

The catch here is that the times may not balance. . . because your actual blackjack game plays to a DISADVANTAGE, you will tend to be on the losing (small bet) side, therefore investing more time.

The fastest way to play it through might be to scale your bets such that the max one-hand investment is half the bankroll. . . assume your game allows splitting and doubling after splits. So a single bet can become 4 bets. . . to bet a max of half stake, your stake must be 8 bets. So if you have a $200 stake, you would bet 1/8 of that, or $25. . . very aggressive! You would need to scale your bets carefully.

Also, there may be a minimum below which you cannot scale your bet. If you drop to $8 -- not that unlikely if you're betting that aggressively, can you still scale to $1 bets? If you drop to $4, can you bet $.50? etc. Also, such aggressive bet scaling will lead to a few very quick session (with enormous bets) and some very long ones (grinding out $100 in bets at $1 a pop is no fun.)

Mind you, scaling the bets is, itself, a time sink. . . calcualting the bet and then entering it by clicking little chip stacks takes a while.

So, where was I? I seem to have wandered. Oh, yeah. . . should you decrease your bet size to lock in the win?

No.