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Best of Alan Krigman

Gaming Guru

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Play Multiple Spots at Blackjack to Moderate Bankroll Swings

20 August 1996

Blackjack buffs can usually pick how many positions to play in each dealing round. Single hands are most common, although quite a few players favor two or even more. There are also the valiant who vary their numbers of spots during a shoe, thinking they'll "change the flow of the cards" and curtail cold streaks or maybe get more hands and exploit hot shoes; however, this is a separate subject which can be deferred for later debate.

The issue for now is, with the same total at risk in a round, whether and how a player's chances are affected by spreading bets across multiple positions. For instance, does betting $5 on each of two spots differ in prospect from $10 on a single hand?

In terms of the player's theoretical loss due to "house advantage," it's all the same. In a game where the rules and a player's decision strategy give the casino a 1 percent edge, the bettor's expectation is to lose a cent on every wagered dollar no matter how the money is allocated.


But expectation anticipates average performance over many hands. And, in low-edge games, only the house sees enough action to satisfy the "law of large numbers." Individuals, even in marathon sessions, are more strongly affected by volatility than edge; that is, fluctuations characteristic of the game induce bankroll swings that normally swamp the impact of house advantage.

Picture what can happen when $10 is bet on a single blackjack spot. a) The player usually wins or loses $10. b) Some decisions are "pushes" and nothing changes hands. c) An uncontested A-10 pays $15. d) With splits and doubles, players increase their exposure but can win or lose $20, $30, or more. e) Insurance and surrender produce occasional $5 outcomes. Together, these factors yield single-spot fluctuation of roughly $11.20 per bet - compared with $0.10 the house "earns" from edge.

What if $10 is split between two spots? Fewer net $10-and-up transactions occur because they require simultaneous wins or losses. Amounts under $10 are won or lost regularly. And pushes, especially due to one winner and one loser, become routine. Edge doesn't change, but fluctuation drops to about $9.70.

The accompanying table gives estimates of how fluctuation falls when a single "bet unit" is spread across multiple positions. Figures for several spots in a single game posit that concurrent bets are partially correlated, owing to the unifying influence of the dealer's hand. For example, everybody who plays properly wins if the dealer busts with an upcard of three through six; nobody wins if the dealer gets a 10-up blackjack.

The table also shows that fluctuation decreases more sharply if money is spread over multiple hands when results are uncorrelated - wholly independent of one another. This situation occurs when several people wager fractions of the same total effective bet at different tables. An illustration would be a couple playing in separate $5 games rather than as a team at one $10 table. Similar conditions apply when a solid citizen plays two $0.25 slots instead of a single $0.50 machine.

Is it good or bad to moderate fluctuation by playing multiple blackjack hands? As often in gambling, the question begs an easy answer. Low fluctuation cuts effective bankroll requirements and can keep players off their fiscal or emotional bottoms during normal downswings. But it also limits the gain during upswings.

Sumner A Ingmark, a muse who moderates his meter but not by penning multiple poems in parallel, pointed out the paradox pithily:

When my luck is running stout,
High fluctuation brings wealth faster.
When my luck has all run out,
Low fluctuation stays disaster.


Table
Characteristic Bankroll Fluctuation per Round
for One Bet Unit Divided among
Different Numbers of Blackjack Hands
Number
of Hands
Fluctuation:
multiple spots,
one game
Fluctuation:
one spot,
multiple games
1
1.12
1.12
2
0.97
0.79
3
0.91
0.64
4
0.88
0.56
5
0.87
0.50
6
0.86
0.46
7
0.85
0.42

 

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.