> > You have $1000 and intend to play blackjack until you
> double the $1000 or go broke. This particular
> blackjack game has a theoretical return of 99.6% with basic
> strategy. You know basic strategy but don't know how
> to count cards. You will be the only one playing and
> the deck will be shuffled after every deal.
> >
> > What is the optimal bet sizing to give you the best
> chance to double the $1000?
> >
> ----------------------------------------------------
> Pretty easy (I think). Bet once - $1000. If U
> bet less every time U R playing @ 99.6%. I'm not
> taking into account chances 2 double & BJ, etc. so I cud
> B wrong.
>
Although I started this post to state that I agreed that this was correct, if you can follow my tedious and confusing logic below, you might decide that I was wrong, and that a single bet of the entire bankroll is NOT correct. This is because the single bet will reduce the return on the game, and doing so MIGHT therefore indicate a different betting strategy that would NOT reduce the return on the game.
Thinking out loud (always dangerous if your thoughts turns out to be stupid - but I find that when I'm done with this post, I'm seeing both sides of the answer, which perhap makes me look stupider, or perhaps saves me)...
If you have ONLY the $1,000, then you won't be able to double down or split pairs, etc., even if that is the correct play -- and therefore you will NOT be able to play correct basic strategy in all circumstances if you bet the whole $1,000 -- and getting the projected 99.6% return presumably depends on actually playing correctly for whatever hand(s) you are dealt, including those that require a double down or a split. Therefore, the theoretical return on the game for a single bet of $1,000 will be less than 99.6%, since you won't be able to make those plays when they are correct.
Still, with MOST bets paying even money, I would think that it would not matter whether the return is 99.6%, or even substantially less, perhaps down to some end point where the game becomes VERY negative (big house edge) - and maybe there is no such end point. It even seems to me that in any game where the most common bet payoff is even money, no matter what the house edge is, if it's a negative game for the player, the correct play to double up or lose it all with a maximum chance of the former would still be to bet it all at once.
If I'm correct, the interesting thing is that this money management strategy would be optimal for a double-up no matter what the house edge is!! It seems a little illogical, but again, if the most common payout is even money, I think it's correct.
If, on the other hand, most bets paid less than even money as the most common payout, then a smaller amount with a double-up after winning seems like it might be the right strategy, while if most bets paid more than even money, I can't envision how it would remain a house-advantage game.
As I say all this, now I can't help but wonder if reducing the expected return on the game by forcing yourself into a situation where you can't always play correctly (ie, by betting all your money at once, precluding correct plays for double downs and pair splits), doesn't in fact change the correct betting strategy -- perhaps the optimal double-up betting strategy MUST preserve the expected return of the game with basic strategy, in which case you WOULD need to bet less and be able to split pairs and double down if indicated. Maybe more than one bet with a preserved option to play correct strategy in all cases and thus a prserved maximum return of the game, is better than a single large bet without that option therefore accompanied by a reduced return.
Maybe I'm too tired to figure this out; I know I've always been told that the best way to double your money at other games is to bet it all, but those are games like roulette, etc., where you just choose the even money bet (even though it is less than 50% to pay off) and bet it all -- but blackjack is a game where betting it all would actually change your strategy options for some of the hands you might receive and reduce the expected return, and therefore the max bet might NOT be correct for such a game.
--BG
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