Yet Another Probability Problem

[AltruismAndCake]

for the first bet you bet $500, and then as long as you lost your most recent bet you bet half of your total money. if you win a bet bet 1/4 your total money.

Assuming you do what you did on post #4, and bet everything after all the loses, and $0 after all the wins, this is a pretty good strategy. If you lose 5 times in a row, you can recover all your money back, but no gain. If you win 5 times in a row, you get around $3662 as your total. If you get LWLWLWLWLW you get a total of $1201, without applying the strategy for the final win. So it would actually earn even more than $1201. For other patterns though, it's a bit weaker, like LLWWLWLWLW will make a total of $667. Again though, if we take into account the final guaranteed win, you would do better. All in all a good strategy, just no guaranteed gains.

Another strat I thought of is start at 1/4 and then every time you lose double your bet and when you win go back down to 1/4

With this strategy you run out of money a bit quick if you lose a few, perhaps a smaller fraction that than starting with a fourth? You were getting really close to my strategy here

Always bet half your money until EITHER:
you have lost 5 times:
Go all in! you can't lose and you'll get back up to 1000!
OR
you have one 5 times:
bet $0 for the rest of the game.

Second part of the strategy is sound, but betting half of your total money each bet is actually one of a few terrible strategies for this game. Without the second part, you are actually guaranteed to lose money with this strategy! The amount you lose is 25% every two rounds you participate in, so $1000 * 0.75^5= $237, if you don't include the second part. The second part of this post gives a major advantage, but I think it's a better fit for one of your other strategies