CasinoCityTimes.com

Gurus
News
Newsletter
Author Home Author Archives Author Books Send to a Friend Search Articles Subscribe
Stay informed with the
NEW Casino City Times newsletter!
Newsletter Signup
Stay informed with the
NEW Casino City Times newsletter!
Recent Articles
Best of Alan Krigman

Gaming Guru

author's picture
 

What Will You Pay to Buy a Sure Thing?

23 November 1998

Casino games have no obscure gambits letting solid citizens make single-stage bets, individually or combined, that either are sure to win or can't lose. Craps and blackjack, however, each have two-step bets offering this feature at the second level. Of course, these apparent gifts from the gambling gods have a hitch.

Here's the craps setup. Bet $12 - laying no odds - on Don't Pass or Don't Come. If the point becomes six or eight, make a Place bet on the same number for $12. On any other point, Place the same number for $10. Possible results are as follows:
* Six/eight - on a seven, Place bets lose $12 and Don't Pass bets win $12 for nets of zero; on the number, Don't Pass bets lose $12 and Place bets win $14 for $2 net gains.
* Five/nine - on a seven, Place bets lose $10 and Don't Pass bets win $12 for $2 net gains; on the number, Don't Pass bets lose $12 and Place bets win $14 for $2 net gains.
* Four/10 - on a seven, Place bets lose $10 and Don't Pass bets win $12 for $2 net gains; on the number, Don't Pass bets lose $12 and Place bets win $18 for $6 net gains.

The blackjack scheme is better known. When you get a blackjack and the dealer has ace-up, buy insurance for half your main bet.

* If the dealer has blackjack, your primary bet pushes and you win 2-to-1 on the half unit insurance; gain is 1 unit.
* If the dealer doesn't have blackjack, your primary bet wins 1.5-to-1 and the half unit insurance loses; gain is 1 unit.

What price do you pay for certainty under these circumstances? It's a sacrifice in the "expectation," the average amount you expect to win over a long time period.

For the craps situation, consider what happens after 990 decisions in each of the cases, anticipating the statistically-correct distribution of results in this many trials.
* Six/eight - the seven and the number should roll 540 and 450 times, respectively. A $12 Don't Pass bet, alone, should therefore win ($12 x 540) = $6,480 and lose ($12 x 450) = $5,400 for a net of $1,080. The two-stage hedge should win ($0 x 540) + ($2 x 450) = $900. You give up an expected $180, an average of over $0.18 per $12 Don't Pass bet.
* Five/nine - the seven and the number should roll 594 and 396 times, respectively. A $12 Don't Pass bet, alone, should therefore win ($12 x 594) = $7,128 and lose ($12 x 396) = $4,752 for a net of $2,376. The two-stage hedge should win ($2 x 594) + ($2 x 396) = $1,980. You give up an expected $396, an average of $0.40 per $12 Don't Pass bet.

* Four/10 - the seven and the number should roll 660 and 330 times, respectively. A $12 Don't Pass bet, alone, should therefore win ($12 x 660) = $7,920 and lose ($12 x 330) = $3,960 for a net of $3,960. The two-stage hedge should win ($2 x 660) + ($6 x 330) = $3,300. You give up an expected $660, an average of about $0.67 per $12 Don't Pass bet.

For the blackjack case, make believe the bet is $10. Consider what happens after 1,300 decisions in which you have a blackjack and the dealer shows an ace-up, assuming the statistically-correct distribution of results. Here, the dealer should and shouldn't have a 10 in the hole 400 and 900 times, respectively. Without insurance, you should push on 400 and win $15 on 900 for a net gain of $13,500. With insurance, you win $10 on all 1,300 for a net gain of $13,000. You give up an expected $500, an average exceeding $0.38 per $10 initial bet.

In these two-stage bets, you've beaten the odds to begin with, just to get into a favorable position. Is it better to take the sure thing, then and there? Or should you risk losing with a gamble offering a greater long-term expected profit? Choose for yourself. Decision scientists would call it a trade-off between utility and probability. And, while you're making up your mind, ponder the pertinent poetry of Sumner A Ingmark.

When you can't afford to lose it,
Take the safe way, don't excuse it;
When the gain outweighs the forfeit,
Go for the expected profit.

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.