So you wanna play blackjack. You haven't learned to count cards and you're deathly afraid of losing your money. You start playing and soon notice that you there is a "back and forth" with winning and losing with you "rarely" losing more than 4 in a row. So what do you do? You do what most rational people will do, you start doubling up after every loss. It works! you're making money until that day you hit "the drop". You have that 5-10 loss in a row and get wiped out of all your money and go home with that "I can't believe that happened" look on your face. What happened?
I did this. I wouldn't accept the math of playing with Mr. Martindale because I did not want to
believe it could happen to me. Let me say up front that you are NOT imagining things. There are many professionals who will laugh at you and tell you that you are falling into some "fallacy" in regards to Mr. Martindale. You are not. Indeed if you graph the number of losses and wins in a row, a pattern does in fact emerge (and must emerge in a truly random game).
The above chart was generated using BJ Apprentice Trainer on IOS. Please note that the random number generator on IOS tends to make this app "Streaky" in that you will notice an either extremely negative variance (lots of losses) or extremely positive variance (a whole lot of winning), but this pattern shows up in actual card games both electronic and live (I have 6 months of win-loss records to prove it).
This one is from another IOS Blackjack app. Same notes as BJ trainer.
What this chart tells you is that your
probability of winning a hand after losing a hand increases by about 50% at each step. It's actually less than that but that's not important here. The issue here is that while your
probability of winning goes up, the
odds of winning are
independent of this probability. In a shoe game with a cut card, the odds go up and down depending on what cards have come out (how card counters play). In a game with a continuously shuffled deck (shuffled after every game, particularly electronic ones) the odds are static from hand to hand and you only have the odds presented at a particular hand as to whether stand, hit, split or double.
Therefore you can be in a situation where though the probability of wining a hand is high (near 98% in some long losing streaks), you can be raising your bets while the odds of winning are particularly low such as a deck with an extremely low count or a continuous shuffled deck in which you got a 16 (not an 8 pair) to a dealer 8.
If you're lucky (have positive variance) your probability of winning will align with the odds of winning or you're beating the odds of losing. On very bad days you end up on the losing side of both probability AND odds.
Now lets look at why a full out Martindale system is so dangerous to your bankroll and why it doesn't even make psychological sense. So in a Martindale progression you start with the table minimum, lets say $5. Each time you lose you double up. At best you have no splits or doubles. so you're doing 5,10,20,40,80,160.320,640,1280... On most $5 tables I've played on you hit table max at $500 so you're effectively cut off after $320. But wait it gets worse for some. Say during this ramp up you end up with a split and double? This happened to me once. I was at the table max had to split and double and ended up with all my money on the table and was beaten by the dealer. It could (and does) happen with card counting as well, but a card counter wouldn't have gotten that high without a seriously favorable situation. However; as discussed earlier with Mr. Martindale I was betting probability and could still be hit by odds (though to be fair the probability of winning doubles, when playing basic strategy is over 50%). Anyway, so you're doing the 5,10, 20...thing and you end up doubling that 20 and losing so you now need to double the 40
ahead of schedule Now you're window has narrowed considerably, say you have to double that $80, you see where this is going.
Lets look at what you risked. You're playing table minimum whenever you're not losing. $5. Say you brought enough money to survive a losing streak that take you to table max and you "give up" at that point and start again at minimum. How much have you lost on a "no split-doubles" situation? At a minimum, before hitting table max you've lost $635. If you played the $500 max on that table as your next hand and lost you're out $1135. And even if you hit it, you would still be behind.
Think about it though, you are willing to risk $1100 for a $5 gain? Not a good look. And if you were willing to part with that much money, why did you sit at a $5 table? Better you went to a high minimum table and flat bet. Really. This is the psychological issue with Mr. Martindale. The person using this, particularly a low roller has a fear of loss mentality yet they risk an outlandish amount of money in order to get a very, very small return. It is a classic example of cognitive dissonance. Stop doing that. A professional gambler understands that you risk short term [small] losses to get long term gains afforded by the math.
So now you're $1100 in the hole and you're back to betting table minimum: $5, do you know how long it will take you to recover an $1100 loss at $5 a pop? 220 straight wins. That's about 1 hour of play. And that assumes you don't have anymore drops or run out of money. Of course you're hoping that doubling, splitting and BlackJacks on the higher bets will get you there faster. It might, odds and probability are against it though. I know. Trust me.
Lets go back to the charts above. Since we see about a 50% increase in probability that you'll win a hand after losing, lets take that out to 5 hands. Even though the probability of any one win streak is actually about 42% we'll round that up to 50% for easy math purposes. So you have 50% probability of winning that first hand. 75% probability of winning the hand after that loss. An 85% probability of winning after that loss. 95% probability of winning after that loss. 97% probability of winning after that loss. Lets look at what that looks like over 100 hands (roughly half hour of play):
50 losses at one win streaks
25 two losses in a row
15 three in a row losses
5 four in a row losses
3 5 losses in a row.
For 200 hands or an hour's play:
100 one hand losses
50 two losses in a row
30 three losses in a row
10 four losses in a row
6 five losses straight.
That's a lot of losses. Put some splits and doubles in there and the losses can mount.
Now lets go back to the psychology. What most people get from this is that when
they play, the 3 five losses in a row per 100/hands will happen sometime near the end of 100 plays. They think that they can play 50 hands and therefore avoid "the drop". It doesn't work that way. If you're lucky (that's positive variance) you'll never see five losses in a row during a session. If you're unlucky the 3 five losses in a row will happen at the top of your play and wipe you out in the first 10 minutes of play. I've had both happen to me. Worse still, since these numbers are
averages, when you account for variance you may well end up with 60 two losses in a row, 20 four losses in a row and 15 five losses in a row. Something that can be particularly devastating to a session bankroll if one uses pushes as a reset.
A note on pushes. How do you account for pushes in a loss in a row scenario. A push is neither a win or a loss. Strictly speaking, the hand after a push is no different than the first hand played in a session. Why? because when you started, there were no wins or losses prior to your hand. This is particularly true in continual shuffle games where odds do not change as cards are dealt. In cut card shoe games this is not as true. We know this because card counting tells us
that when the counts are high, pushes happen more often than in low counts. So if you are unlucky, you lose three times in a row, hit a push, and are sent back to your minimum bet.
Since pushes account for around 10% of events, in a 100 hand game you're going to have your progression stopped cold by a push and you'll be eating that loss. And if that loss is high enough, your minimum bets will not be enough to recover, even with a win streak and you'll slow bleed your bank.
I hope this helps anyone out there who is starting out and thinking of playing with Mr. Martindale.
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