Should You Split your Bankroll into Separate Session Stakes?

Mathematically, gambling is one extended effort. It's the same whether a bettor plays continuously, divides a lifetime into separate casino visits, or splits a specific trip into discrete sessions. And, if the latter, whether the chief exit criterion is time, profit or loss, exhaustion, or a nagging companion.

Folks who think in terms of sessions face the quandary of playing every game from what amounts to a single stash, or breaking their bankrolls into distinct stakes for each sitting. Together with exit criteria, the choice affects short-term prospects.

As with much in gambling, though, the best approach for each solid citizen is a matter of trade-offs and personal preferences. I'll elucidate using double-zero roulette as an example. Similar principles hold for other games - machine as well as table.

Say you visit a casino for a weekend with a $500 gambling budget. You plan to mix about eight hours at the wheel with other activities. You're savvy enough to realize roulette's not a jackpot affair so the only way to win big is to bet big. And, even if you're incredibly lucky, you know you'll never drop $1,000 on a spot and wait for the number to hit and pay $35,000.

You're accordingly not investing your $500 in a long shot at changing your life. Rather, your primary aim is to enjoy the action for those eight hours, racking up rating points so the pit boss will "comp" you for the amenities, and go home with a modest profit or at least some of your original $500.

You have many options, but to illustrate the impact of the bankroll decision in a simple way, picture only two. 1) Jump in with your $500, take breaks when the mood suits you, and restart with whatever bankroll you had when you left off. 2) Divide the $500 into four $125 session stakes and leave the table on an upswing around your two-hour limit, or when the well runs dry. Assume, either way, you bet $1 on each of 10 spots per spin.

Playing with your entire $500 bankroll, you have 90 percent chance of surviving eight hours without going broke. That is, if you try this 100 times, you'll make it 90 and fall by the way 10.

Playing with a $125 stake, your chance of still being in action after two hours is 60 percent. In 100 such sessions, you'll survive 60 and get knocked out in 40. As for enduring eight full hours in four two-hour $125 doses, the chance is only 13 percent - expect it in 13 out of every hundred visits. On the other hand, the probability you'll go belly-up before the end of two hours in all four sessions is only 2.5 percent - fewer than three weekends out of a hundred.

Prospects are lower for surviving separate $125 than integral $500 sessions because of bet sizing considerations. A $10 bet is 8 percent of $125. This is too high for play based on a longevity target. It can yield a good return on the stake if fate is kind, but can be fatal in a mild series of bad calls. Conversely, $10 is 2 percent of $500. This is a fair compromise between the odds of earning a tidy profit and of outlasting a cold streak.

What if you keep the same exit criteria but play at a lower level? Instead of $1 on each of 10 spots, you put a buck on each of five. Now, with a unified $500 bankroll, the likelihood of persisting eight hours jumps to 98 percent. At $125 per session, this strategy raises the potential for seeing two hours of action to 77 percent. The chance of surviving all four two-hour sessions at $125 each is 35 percent; that of crashing every time is only 1 percent. Separate session stakes become more propitious if wagers - and concurrent win goals - are trimmed along with loss limit.

Either way works ... depending on the definition of "works." But splitting a bankroll into session stakes works best if bets are adjusted accordingly. Proving that you can't have your cake and eat it too. Except, maybe, if you stuff an extra piece into your fanny pack at the dessert bar of an all-you-can-eat buffet. The beloved bard, Sumner A Ingmark, had a more sophisticated summary:

Diffusing risk reduces pain,
But also cuts what you can gain.