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
 

There's More to Winning More than Betting More

15 August 2001

Everyone knows the more you bet, the more you win. Or lose. And conversely. But, scaling your play up or down goes beyond raising or lowering betting level. Profit and loss track bet size only if bankroll and win target are varied in the same ratio. As an example, roulette buffs who go from $2 to $10 on each of 10 spots per spin will experience statistically equivalent games, multiplied by five, provided they also buy-in with five times the bankroll and set their exit criteria with five times the profit.

Scaling is a more labyrinthine issue, for instance, when solid citizens seek greater gains by betting more, but don't raise their stakes. Or, as another example, when they lower their bets and buy-ins trying to moderate possible losses, but retain their customary standards for the profit targets at which they'll quit.

The details depend on what and how you play. I'll cite session figures for uniformly-sized blackjack bets with the house having half a percent edge and a game speed of 80 rounds per hour. The accompanying chart illustrates effects of varying bankroll, bet size, and win goal in concert or relative to one another. Entries show two levels of each parameter. Prospects are given in terms of the chance of surviving normal downswings for at least an hour on the specified stake, and -- irrespective of time -- the chance of reaching the earnings target before tapping out.

Effects of scaling bankroll, bet size,
and win goal at blackjack

stake bet size win goal

chance of surviving 80 rounds

chance of reaching win goal
$100 $5 $100 95% 46%
$100 $10 $100 66% 48%
$100 $5 $200 95% 28%
$100 $10 $200 66% 31%
$200 $5 $100 99% 61%
$200 $10 $100 95% 64%
$200 $5 $200 99% 42%
$200 $10 $200 95% 46%

The top and bottom rows show the direct scaling that ensues when the key factors all change in proportion to each other. Folks who buy-in for $100 and bet $5 on every round, or start with $200 and bet $10 per round, share an almost 95 percent likelihood of being in action with their stakes after an hour. If these people persisted until they doubled their money or exhausted their bankrolls, they'd also have equal prospects -- 46 percent probability -- of earning $100 and $200, respectively.

The other rows in the table indicate the mixed bag of changes that occur when the factors vary relative to one another. For instance, say blackjack players used to putting up $100 and betting $5 a pop go to $10 without raising their stakes, and still want $100 profit. The chance of weathering normal cold spells for an hour drops sharply, from 95 percent to 66 percent. Prospects for earning $100 before tapping out grow from 46 percent to 48 percent -- only a small improvement because the benefits of bigger bets are offset by sensitivity to downswings.

Conversely, players might begin with $200 rather than $100 but bet $5 per round. The extra bankroll cushion raises the chance of surviving for at least an hour from 95 percent to over 99 percent. If the goal remains to quit with a profit of $100, the chance of success rises steeply, from 46 percent to 61 percent. Of course, these enhanced session prospects come at a price. Things go awry less often, but they're twice as bad when they do.

Even with proportional scaling, there's a psychological madness to this method. Maybe you're accustomed to a $100 stake and $5 bets. You don't sweat being $80 behind because you know you can make a comeback or, at worse, afford the loss. But you jump to a $500 stake with $25 bets and are $400 down. The chance of recovery is the same. However, $400 is a lot more than $80. At $80, you may keep calm and try to pull out of the hole. At $400, you may panic, quitting in disgust or slamming down a $100 do-or-die bet. This suggests a fourth element to adjust along with bankroll, bet size, and win goal. It's the emotional value, the utility, you assign to different rewards and penalties.

Here's how the poet, Sumner A Ingmark, saw this situation:

You may not make your best decision,
When sums involved becloud your vision.

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.