Martingale Poker
Introduction
The main reason for such a popularity of Martingale strategy is its simplicity and convenience, along with the high chance to make a profit. The main point of this system is to double your investment whenever you lose the bet. For instance, you can place $100, and if you lose, lose the next bet will be $200. The Martingale System for blackjack is premised on a player starting with a low entry bet which is then doubled every time a player encounters a loss. Arguably, a player can recoup all their losses by placing large bets should luck turn to their side. The Martingale is dangerous on every game and in the long run will never win. However it is better to use in baccarat than roulette, just because of the lower house edge. The probability of the player winning 8 times in a row is 0.493163^8 = 1 in 286. Stopped Brownian motion is an example of a martingale. It can model an even coin-toss betting game with the possibility of bankruptcy. The Martingale strategy is a tried and tested way to attempt to mitigate losses in gambling games, but is not always the right solution for poker players. When you lose chips in poker, it is best to stick to your optimum strategy and bide your time, waiting for a good hand with which to recoup your losses.
There can be little debate that the Martingale is one of the oldest and most popular betting systems. The siren's call of the Martingale has fooled many gamblers as it usually results in a session win. However, everybody has a finite supply of money and eventually the Martingale will take down even the biggest of bankrolls.
Rules
The following are the rules of the Martingale.
- The Martingale is generally played on even money bets.
- Start by deciding what your winning goal is and your bankroll size. The great the ratio of bankroll to winning goal, the greater your chances of a session success are.
- To make the math easy, the ratio of bankroll to winning goal should be one less than some power of 2. For example, 7, 15, 31, 63, 127, 255, etc.
- Your first bet should be your winning goal.
- If the result of your last bet is a win, then you have achieved your winning goal and may quit.
- If the result of your last bet is a loss, then double your next bet size, if you can.
- If you can't double your bet because you're busted, then walk away broke.
In other words, keep doubling your previous bet, until you win. As long as you can keep doubling, you will achieve your winning goal eventually. No matter how many losses precede a win, you will achieve your winning goal exactly.
Let's look at an example of a player with a $100 winning goal and a bankroll of $6,300.
Martingale Poker Strategy
- His first bet is $100, which loses.
- His second bet is $200, which loses. He is now down $300.
- His third bet is $400, which loses. He is now down $700.
- His fourth bet is $800, which loses. He is now down $1,500.
- His fourth bet is $1,600, which loses. He is now down $3,100.
- His fourth bet is $3,200, which wins. He is now up $100.
I don't think there is an official procedure if the player doesn't have enough money to double his last losing bet, but still has some money. I suppose what most players would do is bet it all. Then, keep betting the lesser of (1) whatever would be needed for achieve a session win and (2) everything left until either ending marker is achieved.
What to Expect
The following tables show what you can expect to happen under different bets and bankroll sizes. Below is an explanation of each column.
- Maximum Bets — The number of losing bets you can afford to lose.
- Bankroll Units — This is the ratio of bankroll size to winning goal. It is equal to 2maximum bets - 1.
- Probability of Success — Probability of achieving winning goal.
- Average Wins per Loss — Number of units the player can expect to win between losses, assuming he keeps starting over after each session win or loss.
- Probability Doubling Bankroll — Probability of doubling the needed bankroll before going bust, assuming the player keeps starting over after each win.
The first table is based on the Player bet in baccarat. Not counting ties, the probability of the Player bet winning is 49.317517%.
Baccarat — Player Bet
| Maximum Bets | Bankroll Units | Probability Success | Average Wins per Loss | Probability Doubling Bankroll |
|---|---|---|---|---|
| 3 | 7 | 0.869811 | 6.681152 | 0.376682 |
| 4 | 15 | 0.934017 | 14.155437 | 0.359188 |
| 5 | 31 | 0.966558 | 28.902712 | 0.348392 |
| 6 | 63 | 0.983051 | 58.000094 | 0.340634 |
| 7 | 127 | 0.991410 | 115.411214 | 0.334315 |
| 8 | 255 | 0.995646 | 228.687274 | 0.328694 |
| 9 | 511 | 0.997793 | 452.188677 | 0.323417 |
| 10 | 1023 | 0.998882 | 893.172207 | 0.318315 |
Let's look at the situation of the player being able to make up to six losing bets in a row. That would require a bankroll of 63 times the winning goal. The probability of achieving the winning goal of one unit is 98.3051%. If the player did this over and over, he could expect an average of 58.000094 winning sessions for each losing session of 63 units. Note that the loss of 63 units is greater than the 58 wins between losses. Finally, if the player keeps repeating this until he doubles his bankroll, one unit at a time, or goes broke, his probability of doubling his bankroll is 34.0634%.
The next table is based on the pass bet in craps. The probability of the pass bet winning is 244/495 = 49.292929%.
Craps — Pass Bet
| Maximum Bets | Bankroll Units | Probability Success | Average Wins per Loss | Probability Doubling Bankroll |
|---|---|---|---|---|
| 3 | 7 | 0.869622 | 6.669984 | 0.376108 |
| 4 | 15 | 0.933889 | 14.126063 | 0.358450 |
| 5 | 31 | 0.966477 | 28.830284 | 0.347486 |
| 6 | 63 | 0.983001 | 57.828648 | 0.339557 |
| 7 | 127 | 0.991381 | 115.016656 | 0.333066 |
| 8 | 255 | 0.995629 | 227.797787 | 0.327272 |
| 9 | 511 | 0.997784 | 450.214759 | 0.321822 |
| 10 | 1023 | 0.998876 | 888.845840 | 0.316547 |
The next table is based on the don't pass bet in craps. The probability of the don't pass bet winning, not counting ties is 949/1925 = 49.298701%.
Craps — Don't Pass Bet
Martingale Blackjack Odds
| Maximum Bets | Bankroll Units | Probability Success | Average Wins per Loss | Probability Doubling Bankroll |
|---|---|---|---|---|
| 3 | 7 | 0.869666 | 6.672603 | 0.376243 |
| 4 | 15 | 0.933919 | 14.132952 | 0.358623 |
| 5 | 31 | 0.966496 | 28.847268 | 0.347699 |
| 6 | 63 | 0.983013 | 57.868843 | 0.339810 |
| 7 | 127 | 0.991387 | 115.109141 | 0.333359 |
| 8 | 255 | 0.995633 | 228.006247 | 0.327606 |
| 9 | 511 | 0.997786 | 450.677280 | 0.322197 |
| 10 | 1023 | 0.998877 | 889.859390 | 0.316962 |
The next table is based on any even money bet in single-zero roulette. The probability of an even money bet winning is 18/37 = 48.648649%.
Single-Zero Roulette — Any Even Money Bet
| Maximum Bets | Bankroll Units | Probability Success | Average Wins per Loss | Probability Doubling Bankroll |
|---|---|---|---|---|
| 3 | 7 | 0.864588 | 6.384896 | 0.361132 |
| 4 | 15 | 0.930464 | 13.381113 | 0.339231 |
| 5 | 31 | 0.964293 | 27.005325 | 0.323946 |
| 6 | 63 | 0.981664 | 53.536685 | 0.311640 |
| 7 | 127 | 0.990584 | 105.203019 | 0.300746 |
| 8 | 255 | 0.995165 | 205.816405 | 0.290553 |
| 9 | 511 | 0.997517 | 401.747736 | 0.280730 |
| 10 | 1023 | 0.998725 | 783.298223 | 0.271123 |
The next table is based on any even money bet in double-zero roulette. The probability of an even money bet winning is 18/38 = 47.368421%.
Double-Zero Roulette — Any Even Money Bet
| Maximum Bets | Bankroll Units | Probability Success | Average Wins per Loss | Probability Doubling Bankroll |
|---|---|---|---|---|
| 3 | 7 | 0.854206 | 5.859000 | 0.331848 |
| 4 | 15 | 0.923266 | 12.032100 | 0.301929 |
| 5 | 31 | 0.959614 | 23.760990 | 0.278607 |
| 6 | 63 | 0.978744 | 46.045881 | 0.258320 |
| 7 | 127 | 0.988813 | 88.387174 | 0.239598 |
| 8 | 255 | 0.994112 | 168.835630 | 0.221820 |
| 9 | 511 | 0.996901 | 321.687698 | 0.204736 |
| 10 | 1023 | 0.998369 | 612.106626 | 0.188263 |
Video
Please enjoy my video on the Martingale.
Summary
If you want to maximize your chances at a session win, then your chances of achieving it are best with the Martingale. This is at the expense of very short sessions (so less fun playing) and abject disaster when things go bad.
Like all betting systems, not only won't the Martingale eliminate the house edge, it won't even dent it. The expected ratio of losses to amount bet will approach the house edge the more you play. If you must use a betting system, please use a free one like the Martingale. Never pay for one, as they are all equally worthless mathematically.
Internal Links
- The Truth about Betting Systems.
- Labouchere betting system.
- Fibonacci betting system.
- D'Alembert betting system.
- Oscar's Grind betting system.
Written by: Michael Shackleford