• Kitchen Martingale Betting System
• Martingale System Sports Betting
• Craps Martingale Strategy

R/Craps: Craps is a dice game in which players place wagers on the outcome of the roll, or a series of rolls, of a pair of dice. Martingale Betting System, 4-1. Martingale betting yields a good shot at a modest gain, offset by a small chance of a big loss. Averaged over many players, losses outpace wins by the aggregate forecast from edge and gross wager. In a recent column about craps, I discussed pros and cons of successive Come bets without odds as alternatives to Placing multiple numbers for. Nearly every gambling expert likes to cite Martingale as an example of a losing system and then jump into a gloating mode and proclaim that all betting systems are losers. However, a Martingale system can be used with very good results if it is used on a spot basis.

• The Martingale Strategy is a highly debated betting strategy that some bettors swear their millions by and can best be applied to games of 50% chance such as a coin toss or roulette. Others denounce it as purely theoretical and not able to be replicated in a real casino setting. We’re here to settle that debate once and for all.
• Craps; The Problems with the Martingale System. The Martingale Strategy is a tantalising betting system, for good reason, and in a vacuum, it works to a tee. Its mathematical principles are sound as can be, and the strategy is logical and sensical enough that make them easily applicable to many casino games.

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So I had an idea (probably been thought of before, but meh) of a martingale esque system that if you have a good chunk of capitol to start with, should pay out very well. All you do, is start with the minimum, and play just the field bet. Any time you dont win, you triple the bet. The way I figure it, this should pay off prety well.
Bet amount Win amount total investment profit in series
$5 10 5 5
$15 30 20 10
$45 90 65 25
$135 270 200 70
$405 810 605 205
1000 (MAX) 2000 1605 395
Thoughts?

The interesting thing about this system is that you almost want to come to a point of near failure before you win because that is the time that you have any chance of winning any kind of substantial amount of money. I'm also assuming that either Midnight or Snake Eyes pays triple, though it doesn't seem that you mentioned that. Now, the Field Bet is a bad bet compared to most (except at Santa Ana Star where both Snake Eyes and Midnight pay triple for a House Edge of 0.00%,) but it becomes a horrible bet if the House only doubles Midnight and Snake Eyes.
It's like any other Martingale, otherwise. The only difference is that I can't compare it to making one large bet to win a fixed small amount, because the amount to be won is not fixed, so let's do some Math...
(NOTE: My computer is being funky about multiple windows, so I'm using an actual scientific calculator and moving stuff over, so I may screw up a minor decimal place)
$5.00 Field
Probability of Even Money: 14/36
Probability of Double: 1/36
Probability of Triple: 1/36
Probability of Loss: 20/36
Even Money: 1.9444444
Double: .27777778
Triple: .416666667
1.94444444 + .27777778 + .416666667 = 2.638888887
$15.00 Field (if loss)
Probability of Even Money: (14/36 * 15)
Probability of Double: (1/36 * 30)
Probability of Triple: (1/36 * 45)
Probability of Loss: 20/36
Even Money: 5.833333333
Double: .833333333
Triple: 1.25
(1.25 + .8333333333 + 5.833333333 - 5) * 20/36 = 1.62037037
$45.00 Field (if two losses)
Probability of Even Money: (14/36 * 45)
Probability of Double: (1/36 * 90)
Probability of Triple: (1/36 * 135)
Probability of Loss: 20/36
Even Money: 17.5
Double: 2.5
Triple: 3.75
(3.75 + 2.5 + 17.5 - 20) * (20/36 * 20/36) = 1.15740741
$135.00 Field (if three losses)
Probability of Even Money: (14/36 * 135)
Probability of Double: (1/36 * 270)
Probability of Triple: (1/36 * 405)

Kitchen Martingale Betting System

Probability of Loss: 20/36
Even Money: 52.5
Double: 7.5
Triple: 11.25
(52.5 + 7.5 + 11.25 - 65) * (20/36 * 20/36 * 20/36) = 1.071673525

Martingale System Sports Betting

$405.00 Field (if four losses)
Probability of Even Money: (14/36 * 405)
Probability of Double: (1/36 * 810)
Probability of Triple: (1/36 * 1215)
Probability of Loss: 20/36
Even Money: 157.5
Double: 22.5
Triple: 33.75
(33.75 + 22.5 + 157.5 - 200) * (20/36 * 20/36 * 20/36 * 20/36) = 1.309823198
$1000.00 Field (if five losses)
Probability of Even Money: (14/36 * 1000)

Craps Martingale Strategy

Probability of Double: (1/36 * 2000)
Probability of Triple: (1/36 * 3000)
Probability of Loss:
Even Money: 388.8888889
Double: 55.5555556
Triple: 83.3333333
(83.3333333 + 55.5555556 + 388.8888889 - 605) * (20/36 * 20/36 * 20/36 * 20/36 * 20/36) = -4.08676598
Six Losses
(20/36^6) * -1605 = -47.18891655
Expected Value of Total Bet: -47.18891655 - 4.08676598 +1.309823198 + 1.071673525 + 1.15740741 + 1.62037037 + 2.638888887 = -$43.47751914
Worthy of note is that it appears (to me) that you should stop at the $405.00 bet if the Table Maximum prohibits you from making a bet of $1215. I mean, the House Edge is the same either way, but even ignoring a loss, the combined expected value of all of your potential wins on the $1,000 bet doesn't even cover the amount that you have already lost.

WHat do you guys think about employing the same 'triple up' idea at baccarat or some other 'coin flip' type set up, whether it be baccarat, playing red/black on roulette, etc.

I think that your long-term losses will fall in line with the House Edge of the game.
Honestly, though, the idea behind any sort of negative progression system is to be able to lose at a higher than expected rate and still come out ahead, so the Field Bet would not be my choice because it has a higher loss rate than many other Even-Money propositions. The higher loss rate makes it more likely that your system will fail.
The thing that you will lose not betting the Field is the ability to Double or Triple the amount bet on a win, but if you were to apply your system to something with a lower loss rate, such as a Line Bet at Craps or Baccarat, then you will lose less often. Those bets also come with a Lower House Edge, which always makes them better regardless of what system you are playing or none at all...as your losses will always approach the House Edge.
For example, the Pass Line bet at Craps has a .5071 probability of losing, so your probability of dropping six in a row is:
(.5071)^6 = .017004414
Which makes your success rate:
1 - .017004414 = .982995586 or 98.3%