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Best of Alan Krigman

Gaming Guru

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Picture the Impact of Your Bets Using 50-50 Equivalents

17 May 1999

All casino bets are associated with one or a set of chances to win, and the associated payouts. With so many choices, everyone wants to know which are best. Easy to ask, tough to answer.

To illustrate, consider equal bets at double-zero roulette on 12-number columns and three-number rows. The columns have 31.58 percent chance to win and pay 2-to-1; the rows have 7.89 percent chance to win and pay 11-to-1. How do you tell which is better?

The usual approach is to compare edge or house advantage. This is generally of dubious value to players because it's a long-term effect with relatively small influence during sessions of reasonable length. It's totally useless here because the bets have equal edge, yet still obviously affect sessions differently. One way the impacts differ is that longer odds on the rows mean more radical bankroll swings. And, even this can be good or bad.

For instance, with these particular wagers, assume players start with $200 and bet $5 per spin, continuing until they've got $400 or go broke. The chance of success is only 10 percent with the columns and 40 percent with the rows. Instead, assume the same players go for 100 spins, come hell or high water. Then, the columns offer under 1 percent chance of ending $200 or more in the hole while the rows yield 14 percent chance of doing so.

Complexity compounds when comparing bets with variable payouts. These might be five coins in a $1 video poker machine returning $5 to $4,000, versus $5 at blackjack where most wins are $5 and a few are more. Edgewise, blackjack usually beats video poker. But say that skilled players at each game start with $200 and try to double their money without tapping out. They have 42 percent chance of success at blackjack and 47 percent at video poker.

Last week, I showed how to compare disparate bets using their "even-money equivalents." These were the theoretical amounts of and chances of winning bets with 1-to-1 payouts, with the same impact on bankroll as money actually wagered in the game. The approach showed, for instance, that $5 on a 12-number column is equivalent to betting $7 for even-money with 48.11 percent chance of winning. Similarly, the even-money equivalent of $5 on a row is $16.20 with a 49.19 percent chance of winning. The latter is therefore like putting more at risk and winning more often.

Another yardstick some solid citizens might find helpful is the "50-50 equivalent." This is a bet-payoff pair with a 50-50 chance of winning, that has the same impact on bankroll as $1 actually wagered in the game. The following list shows theoretical 50-50 equivalents for some representative cases.

 wager  equivalent bet  equivalent payoff
craps    
place six/eight  1.09 1.06
place five/nine 1.22 1.14
place four/10 1.39 1.25
any craps proposition 2.62 2.40
three/11 proposition 3.78 3.55
two/12 proposition 5.23 4.96
double-zero roulette    
outside (lose half on 0 or 00) 1.01 0.95
12-number column 1.45 1.34
four-number corner 2.81 2.71
three-number row 3.28 3.18
single number 5.81 5.71
blackjack    
played with 0.5% house edge 1.13 1.12
played with 1.0% house edge 1.13 1.11
 played with 1.5% house edge 1.14 1.11
slot machines    
typical 97.3% video poker  4.42 4.37
typical 95% three-reeler 7.08 6.98

Envision the figures in the table like a coin toss. On the indicated video poker machine, $5 is equivalent to a flip where $5 x 4.42 = $22.10 wins $5 x 4.37 = $21.85. At 1-percent blackjack, it's like flipping a coin for $5 x 1.13 = $5.65 to win $5 x 1.12 = $5.60. With such equivalents, you needn't be a Nikolai Ivanovich Lobachevski to grasp both what's siphoned off to house edge and the magnitudes of the fluctuations a bankroll will undergo. Nor need you belong to the Sumner A Ingmark Poet and Peasant Society to grasp what the bard meant by writing:

The more of your reserve you trust to chance,
The sooner you'll go broke or wealth enhance.
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.