The Odds Determine Your Overall Fate in Gambling

As time goes by, the gambling questions I receive begin to repeat themselves. Here are a few of the more interesting ones, all illustrating that the odds determine your overall fate in gambling:

Dear Fred,

I know most gaming authors don't approve of betting systems. But how about this: Why shouldn't I be able to go on winning a small amount at Roulette by consistently betting $5 on "black", and just doubling my bet every time I lose? Some casinos even have $5000 limits, leaving room for 11 losses in a row before reaching that ceiling. Even when I lose 5 straight and win the 6th, I'm $5 ahead for those 6 bets. Then I just go back to $5 and start over again. It's worked so far, though I've had some tense moments.

Dear Double up,

The betting system you describe is the notorious "Martingale". With it, you bet one unit and keep betting one unit if you win -- but double up after each loss until you finally win. Doing that, any string off losses will be totally wiped out and replaced with a one-unit net gain by that next win. Then you revert back to one unit. It's a provocative, tantalizing scheme -- seemingly foolproof. However, here are the pertinent factors.

• The Martingale System will in fact show a total net profit of one unit for every bet won during a session, regardless of the losses in between.
• A roulette wheel makes about 40 spins per hour, 19 of which should be black. Betting $5 basic units, you should indeed net $5 x 19 blacks, or $95 per hour unless you hit a fatal losing streak.
• Financing the Martingale up to 11 consecutive losses will require $10,115. Probability says you should lose 11 (or more) in a row once every 2459 spins of the wheel or every 62 hours.
• If all went typically, you'd win $5800 in 61 hours, then lose ten grand when the hammer falls.
• Even if you could double up out to infinity, you'd still have no edge! You'd always be more likely to hit a streak that will cost more dollars than you've won thus far. And what if it doesn't end? Remember, if we're talking infinite bankroll, then we're talking infinite losing streaks too.

Mr. Renzey,

What's wrong with the strategy of two partners going to the craps table, one betting the pass line and the other the "don't", each for $100, and playing just for the cash comps? Together, we'll receive $20-$30 per hour in redeemable cash coupons (local riverboats here pay you comps in cash commensurate with your gambling volume).

Dear Hedge,

Betting both sides of the line is not a money-saving strategy. Over time, the two of you will break even on 35 rolls out of 36, then lose $100 that 36th time when box cars comes up ("pass" loses but "don't" pushes). At 45 pass decisions per hour, that'll cost you and your partner a combined average of $125 per hour. Look at it this way. Suppose you and a total stranger just happened to be betting opposite sides of the line for a C-note apiece. The house has a 1.4% edge on each of those bets, so you're both supposed to lose money individually. Afterwards, if you just happened to bump into each other at the buffet and decided to pool your results, how are you going to be any better off?

Dear Fred,

I enjoyed your last poker article outlining 7 Card Stud basic strategy on the fifth card. But I was troubled by your advice to fold a pair of 10s just because you think somebody has a pair of Jacks. Why fold in such a close situation when there are still two more cards coming? Can you elaborate?

Dear Stud,

You should fold most underpairs with no overcards (such as having 10-10-8-5-3 against J-J-6-2-Q) because you won't win often enough to cover the cost of going all the way. Too often you'll make, say, 10s and 8s only to lose to something like jacks and deuces. A breakdown for playing your hand out 100 times follows:

Even counting the previous money that's already in an average-sized pot, winning just 29% of these hands will make you an overall loser. Only if there's serious doubt that your opponent actually has the jacks, or if his other cards are very dead and yours are live, can you call.

Fred Renzey,

I don't follow the rationale of doubling down with a soft 18 in blackjack -- even against a dealer's bad up-card. If you could substantiate its merits, I'd be most grateful.

Dear Soft 18,

Here's a comparison of how you'll do standing versus doubling 100 times each with Ace/7 against a dealer's 6:

Standing, you'll win 28 more times than you'll lose. Doubling, you'll win only 19 more times than you'll lose, but for 2 bets each and a 38 bet gain. 'Nuff said.