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Best of Alan Krigman

Gaming Guru

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Should You Divide Your Bankroll into Session Stakes?

2 October 2000

Good gamblers set sail on casino campaigns with betting budgets above which they do not deviate. But even the gurus disagree whether to risk the whole shebang on each and every foray, or to split a bankroll into separate stakes for specific sorties.

Intuitively, the trade-offs are clear. Consolidated bankrolls help solid citizens -- those able to take the heat, anyway -- climb out of the normal holes they should expect at the machines or tables. But sporadic severe cold streaks can take them totally out of action. Apportioned stakes may result in more games ending early. Yet they leave bettors -- those undeterred when they don't at first succeed -- with the resources to try, try again.

As usual in gambling, there's no one right method. Personal predilection enters the decision process. And what works wonderfully on one occasion may misfire miserably on the next.

The spectrum of options can be examined using actual numbers rather than seat-of-the-pants speculation. Figures for a representative situation show magnitudes of typical gains and sacrifices, and can help you evolve an approach that best suits your particular preferences.

Make believe you're planning a weekend of $10 blackjack with a $500 bankroll. You hope to play about 10 hours -- 800 rounds. Consider three bankroll alternatives: (1) Buy in at the first table for the full $500; continue for the weekend treating this money, plus any winnings and minus any losses, as a single bankroll. (2) Split the $500 into two $250 stakes; play on the first until it's gone or doubled, then start afresh, following the same criteria on the second. (3) Divide the $500 into five $100 segments; play on the first until it's gone or doubled, then repeat this process on each of the remaining four stakes.

One way to quantitatively compare these money management methods is to calculate the probability of weathering the downswings you can expect during sessions of length proportionate to the buy-in. Values can be found by survival-based "risk of ruin" analysis. With the full $500 at risk, a proficient Basic Strategy player betting $10 has 84 percent chance of being in action after 800 rounds. The same person with a $250 session stake has 69 percent chance of surviving 400 rounds at $10 each. Starting with $100, this bettor has 49 percent chance of outlasting 160 $10 rounds.

A second means of weighing the alternate approaches is to determine the chance of doubling the buy-in, betting $10 per round, independently of how long it takes to either achieve this win goal or deplete the stake. Here, figures can be determined by profit-based "risk of ruin" analysis. Considering the entire weekend as a single session, the player has about 35 percent chance to win $500 rather than lose the same amount. Splitting the visit into two parts, the bettor has 42 percent chance to win $250 as opposed to lose this much in each segment. And dividing the trip into five portions, the individual has 47 percent chance of earning $100 before losing a like amount in each session.

The first set of probabilities suggests the extent to which dividing a bankroll into session stakes reduces the prospects of surviving individual proportionately shorter games. The second set indicates how playing multiple lower-stake sessions improves chances of reaching correspondingly less lofty earnings goals.

Which is best for you? If you'll really rue a premature wipe-out, divide your money into session stakes but accept the low returns each sitting is apt to yield. If you won't be satisfied with a modest payday, play with a consolidated bankroll but accept the diminished likelihood of success.

Much of gambling skill involves understanding the constraints imposed by the laws of chance. But, understanding doesn't burst the constraints to get those laws to work both ways. You can get them on your side if you know the way you want to go. Or, you can always get lucky. As the bettors' bard, Sumner A Ingmark, said:

                Making progress incrementally,

               May get you far, coincidentally.

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.