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Best of Alan Krigman

Gaming Guru

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The Hows and Whys of First-Level Bets at Let It Ride

14 June 1999

In Let It Ride, players often take unwarranted risks at the first level, with three cards known, believing they can cut their losses at the next stage if necessary. The optimum strategy is to keep first-level bets in play only under two sets of conditions:

  1. "Made" hands -- pairs of 10s through aces or any triplets.
  2. Possible straight flushes -- with no gaps if the lowest card is three or higher (e.g., 4H-5H-6H), one gap if at least one card is 10 or higher (e.g., 8C-9C-JC), and two gaps if at least two cards are 10 or higher (e.g., 8D-10D-QD).

"Made" hands are money in the bank. The others, the prescribed incipient straight flushes, don't always win. But they're all favorable, and yield greatest expected profit with first-level bets active. Most embryonic straight flushes which should be bypassed at this stage are also favorable even with the bet riding; however, the edge is greater when it is reclaimed owing to the order in which the two community cards are exposed and the effect of decisions at the second level, with four cards known.

In principle, you can win with any starting hand. The worst case would be three unsuited and unpaired low cards, enough apart to preclude a straight. An illustration might be 4H-6D-9D. Here, the dealer has 2.5 percent chance of turning over a high pair for a 1-to-1 payoff, 2.3 percent chance of exposing cards that match two of yours to form two pair and pay 2-to-1, and 0.8 percent chance of uncovering a pair that forms a triplet with something in your hand for a 3-to-1 return. The other 94.4 percent are losers. The low probabilities and small payoffs make it less onerous to withdraw the first-level wager than to take a shot.

Prospects improve if unsuited starting hands have at least one high card, can finish with a straight, or include a low pair. In the latter case, for instance, you could end up with four of a kind paying 50-to-1, a full house returning 11-to-1, triplets at 3-to-1, or two pair for 2-to-1. But chance of winning is still only about 25 percent, and expectation is greater withdrawing than risking your first-level bet. Likewise, three suited cards, separated enough so they can't yield a straight, can form a flush but aren't promising enough to justify the first-level bet.

Your chances of a winning session are best if you let bets ride only when dogma dictates. You might miss a few fortuitous flops, but -- across many hands -- the odd bonus is more than offset by frequent forfeitures. Further, the hands in question can't form royals, so they don't rate as longshots at jackpot-size payoffs.

The following figures were derived by gaming guru, Stanley Ko. They show theoretical penalties for leaving first-level bets in action when statistics say take them down. Amounts are based on starting with $1 in each spot. Multiply up for your actual bet.

hand win or loss 1st level bet in action ($) win or loss 1st level bet taken down ($) penalty ($)
4C-6S-9H -1.70 -0.85 0.85
5H-6D-7C -1.08 -0.54 0.54
6C-7D-QS -1.24 -0.59 0.65
9D-10D-JH -0.23 -0.02 0.21
QS-KD-AH -0.15 +0.04 0.19
4S-4H-7H +0.23 +0.29 0.06

As an example of interpreting the data, assume you're dealt 6C-7D-QS. For every set of $1 initial bets, you can expect to lose $1.24 if you keep the first-level wager in action and $0.59 if you reclaim it; the penalty for violating the optimum strategy is $1.24 - $0.59 = $0.65. If you start a round at $10 per spot, this translates into a $6.50 gift to the casino bosses.

Most hands calling for removal of first-level bets are net losers no matter how they're played, but worse with the wagers alive. Others are underdogs with first level bets in place and favorites if they're withdrawn. A small group has positive expectation either way, but promises higher profit without the first-level wagers. Theoretical penalties for first-level indulgence run from under $0.03 to $0.85 starting with a dollar on each of the three spots. And there's no carrot dangling on the stick to tease you with a big return. As the pennywise poet, Sumner A Ingmark, said:

Unless rewards are truly massive,
It's best to follow tactics passive.
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.