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Best of Alan Krigman

Gaming Guru

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Here's a Simple Worksheet to Estimate Bankroll Needs

19 February 2002

Nothing crimps a gambler's style as badly as depleting a bankroll and lacking the wherewithal to scamper out of a hole. Sometimes, it can't be avoided. A player does right but a cold streak pushes the envelope of what ought to be the normal downswings. Far more often, premature ruin results from inadequately staking a betting strategy. Granted, there's a dilemma. It's most overt when viewed bottom-up, from a bet sizing perspective. Low bets help players survive cold spells, but may not satisfy their profit goals. High bets can yield fat gains, but too readily lead to bankruptcy.

Set aside, for now, the issue of winning enough to quit your day job. Then, it's possible to develop bankroll criteria for various situations based entirely on the specifics of a game and the confidence you'd like that your stake will suffice for a session of reasonable duration. And, they're not just one guru's opinion versus another's; they're a matter of rigorous statistics.

If you insist on precise values, though, the math gets hairy. Fortunately, for most gambling purposes, ballpark estimates are more than ample. With this in mind, I devised the accompanying worksheet. Copy it for future use. It gives bankroll, as a number of nominal bets, to have a desired confidence in not busting out before completing some set of rounds. The worksheet only requires two easy multiplications and one addition, and gives a figure reliable enough for moderate-length sessions in typical games.

Bankroll Estimation Worksheet
Factor Evaluation Result
Edge (edge in % x 2) ___________
Rounds (rounds x 0.07) ___________
Volatility (flat, even-money: 0)
(otherwise: 65)
___________
Confidence (90% confidence: 30)
(95% confidence: 35)
(99% confidence: 40)
___________
TOTAL (add results) ___________

 

To apply the worksheet, the sole detail you need about the game and your choice of bets is house edge. Use it if you know it. Otherwise, take 1 percent for blackjack and baccarat; 1 percent for craps assuming mostly line and come bets with odds, 3 percent otherwise; 5 percent for all other table games and video poker; and 7 percent for reel-type slots. Evaluate the edge, rounds, volatility, and confidence factors according to the worksheet, and add up the answers. Use whole numbers; get rid of decimal fractions by taking the next higher integer. The total is the recommended bankroll, expressed as a number of base bets.

Here's an example of how to use the worksheet. Say you want to play roulette with 95 percent confidence of lasting for 100 spins, and will make both inside and outside bets - progressing if you hit a run - so your game is volatile. You'd fill out the worksheet as indicated. The total, 116, means that a $10 gross wager such as $5 on red and $1 on each of five black spots would require $10x116 or $1,160. Too much? Skipping the outside bets, the amount drops to $5x116 or $580. Betting $10 flat outside, volatility is 0 instead of 64 so you should have $10x52 or $520. Want 99 percent confidence on outside $10 bets? Use 40 instead of 35 for the confidence factor to get $10x57 or $570.

Sample Bankroll Estimation Worksheet for Roulette Example
Factor Evaluation
Result
Edge (5 x 2)
10
Rounds (100 x 0.07)
7
Volatility (Volatile: 64)
64
Confidence (95% confidence: 35)
35
TOTAL (add results)
116

 

Democrats as well as Republicans might want to know how I derived the worksheet. I evaluated "risk of ruin" equations for a raft of conditions, then used a "multiple regression" to get the indicated constants. There's a wide margin of error, but it's not critical because rational players would buy-in for something convenient like $500, regardless of whether the actual suggested bankroll was $10x46 = $460, $10x49 = $490, or $5x104 = $520.

Many solid citizens are surprised at the money needed for a high level of confidence in surviving normal downswings. But no more astonished than folks who start with less than their wagers warrant and wonder where it all went. The latter mob might well be motivated to mutter the mantra of the muse, Sumner A Ingmark:

A gambler shorthanded,
Is often left stranded.

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.