Can you guarantee a win on a true 50/50

I was thinking of a +4,-3 progression with different rules for consecutive wins and losses but I just realized testing the different first 51 outcomes is not as easy as I thought :(

Quote: stevenm0519

I was thinking of a +4,-3 progression with different rules for consecutive wins and losses but I just realized testing the different first 51 outcomes is not as easy as I thought :(

This is a scary statement... You DON'T BEAT CASINO GAMES WITH BETTING SYSTEMS. You must tract the house edge in a game that swings from side to side (such as your red/black deck example) and you must bet on the ADVANTAGE. Betting systems WILL NOT win unless your betting system is "bet more on color X when there's more of those left int he deck!"

Please take notice since you asked the question on page 1 how many people have chimed in with a "betting system" of some type where your bets have nothing to do with the actual cards removed?

Quote: stevenm0519

I was thinking of a +4,-3 progression with different rules for consecutive wins and losses but I just realized testing the different first 51 outcomes is not as easy as I thought :(

It's typically not super easy to figure this kind of stuff out...because it can branch out many different ways (ie: RBRBRBRB, RRBBRRBB, RBRRBRBBRBR....etc).


And I really hope you don't try/practice with this type of an example of a betting system based on wins & losses. Unfortunately, under these circumstances (the way the game is played and cards are removed), I think it'd be possible for someone to try to beat it using a betting system -- where they increase their winnings when on a losing streak -- which would (likely) end up being profitable for the player due to the removal of the cards and shifting advantage.

IOW: If you played this game and used a betting system, you'd probably win but not because of the betting system, but because the game is flawed.

Quote: RS

IOW: If you played this game and used a betting system, you'd probably win but not because of the betting system, but because the game is flawed.

Actually, a Martingale on black can guarantee a win in a game like this one without independent trials. All you'd have to do is bet a Martingale on black until you've won 26 units, then stop betting because there are no more black cards to win with. Regardless of the permutation of the cards in the deck, you'll always win 26 units.

But the reason you win is because the game doesn't use independent trials, not because the odds (off the top) are 50/50. If you wrote "red" and "black" on two sides of a coin and flipped it 52 times, the same Martingale on black couldn't guarantee a win. Selection without replacement is required.

Quote: stevenm0519

If you have a deck of cards with betting whether the next card will be red or black. What is the best way to maximize profit on a $5 minimum $500 max with a $500 bankroll?

There is no way to maximize winnings on a fair bet. You are equally likely to win as lose. Your EV is 0, so you would expect to break-even over the long term

Anyone know how to calculate the different wlwlw combinations for 52 bets?

Yes.
Define your calling strategy.

Quote: stevenm0519

Anyone know how to calculate the different wlwlw combinations for 52 bets?

There are 52! / (26! x 26!) = 495,918,532,948,104 different ways.
If you mean, how do you list them all out, I can't think of any way other than brute force - for example, let the black cards be in positions:
1, 2, 3, 4, ..., 24, 25, 26
1, 2, 3, 4, ..., 24, 25, 27
1, 2, 3, 4, ..., 24, 25, 28
...
1, 2, 3, 4, ..., 24, 25, 51
1, 2, 3, 4, ..., 24, 25, 52
1, 2, 3, 4, ..., 24, 26, 27
1, 2, 3, 4, ..., 24, 26, 28
...
1, 2, 3, 4, ..., 24, 26, 52
and so on, until you finally get to
27, 28, 29, ..., 51, 52
Actually, you only need to look at the ones that begin with 1; each one has a "partner" consisting of the other 26 numbers. (Every ordering has a "partner" ordering where the black and red cards are reversed; exactly one ordering in each pair has the desired color as card 1.)