4 vs 6 Bankers: Comparing Line Counts and Failure Risk

A “banker” is any selection you’re confident enough to fix permanently into every line of a permutation, rather than leaving it inside the combinatorial pool. Bankers are a cost-control tool: the more matches you lock in as fixed, the fewer lines you need to cover the remaining selections. But that same fixing is also where the risk concentrates, because a banker that doesn’t come in can take out every single line built around it. Deciding how many to use is really a trade-off between affordability and fragility, and it’s worth working through the numbers rather than guessing.

Setting Up the Comparison

Assume, for the sake of a clean comparison, that you’ve identified twelve matches you’re happy to include across your coupon, and you want to settle on a structure. Two realistic approaches, both genuine reduction perms rather than single combined lines:

Both numbers check out by direct calculation: C(8,6) equals C(8,2), which is (8×7)/2 = 28. C(6,4) equals C(6,2), which is (6×5)/2 = 15.

What the Line Counts Actually Mean

Option B is cheaper — 15 lines instead of 28 — because fixing two extra bankers removes two matches from the combinatorial pool entirely, shrinking the maths considerably. At an illustrative stake of 15p per line, Option A costs £4.20 and Option B costs £2.25. That’s a meaningful saving if you’re running several perms across a coupon every week.

But the saving comes at a cost in resilience. In Option A, you’re trusting only 4 bankers to come in regardless of what happens elsewhere; if one of those 4 fails, every one of your 28 lines fails with it, but you were only ever relying on 4 “must-win” judgements. In Option B, you’re trusting 6 bankers — half again as many opportunities for one of them to go wrong, and because every single line in that perm depends on all 6 holding up, your entire £2.25 outlay is hostage to six independent results instead of four.

A simple way to frame the trade-off

If each banker has, illustratively, an 80% independent chance of landing the result you need, then the probability all 4 bankers land together is 0.8⁴ ≈ 0.41, or about 41%. Extend that to 6 bankers at the same illustrative 80% each, and the probability all 6 land together drops to 0.8⁶ ≈ 0.26, or about 26%. Even though Option B is cheaper per line, the chance that your bankers survive intact falls sharply as you add more of them — which is the real cost that a lower stake total disguises.

A Third Structure: Splitting the Difference

Between the two extremes sits a middle option worth calculating properly rather than guessing at: 5 bankers fixed, with a 5 from 7 perm covering the remaining selections. That gives C(7,5) = C(7,2) = (7×6)/2 = 21 lines — cheaper than Option A’s 28 lines, more expensive than Option B’s 15, and critically, resting on 5 banker judgements rather than either 4 or 6. At the same illustrative 80% independent success rate used earlier, the probability of all 5 bankers landing together is 0.8⁵ ≈ 0.328, or about 33% — sitting neatly between Option A’s roughly 41% and Option B’s roughly 26%.

Laid out this way, the trade-off is visibly smooth rather than a binary choice — each additional banker you fix buys a specific, calculable reduction in cost against a specific, calculable reduction in the odds that your whole perm survives intact. There’s no objectively correct point on that scale; there’s only the point that matches how confident you genuinely are in your selections and how much you’re comfortable risking on that confidence being right.

Choosing Between Them

Neither option is objectively better; it depends on how confident you genuinely are in each selection and how much weekly outlay you’re comfortable with. As a general rule:

• Use more bankers when you have a small number of selections you’re unusually confident about and want to minimise cost.
• Use fewer bankers, with a larger reduction pool, when your confidence is spread more evenly across your selections and you’d rather diversify risk than concentrate it.
• Always recalculate the line count before staking — it’s easy to misjudge how quickly combinations grow or shrink as you move bankers in and out.
• Remember the illustrative percentages above are just that — illustrative. Real match outcomes don’t come with a neat probability attached.

Checking Your Workings

Whichever structure you land on, it’s worth re-deriving the line count independently before staking, rather than trusting a single calculation. A quick cross-check: C(8,6) and C(8,2) should give identical answers by the symmetry rule, since choosing 6 to include from 8 is equivalent to choosing 2 to leave out. C(8,2) = (8×7)/2 = 28, matching the figure used above. Running the same check on C(6,4) against C(6,2) gives (6×5)/2 = 15, also matching. If your own arithmetic on a different perm size doesn’t match when checked both ways, that’s a sign of an error worth finding before you commit real stakes to it, not after.

It’s also worth sanity-checking your figures against a published perm chart where one’s available, since those charts are produced specifically to let you cross-reference your own working rather than trust a single calculation blind.

Whichever structure you settle on, stick to a stake you’ve budgeted in advance and treat the pools as entertainment rather than an investment. It’s 18+ only, and if the weekly habit ever starts to feel like a pressure rather than a pastime, services such as BeGambleAware are there to help. A perm is a planning tool for managing cost and coverage, not a shortcut to beating the odds — no banker structure changes the underlying uncertainty of the football itself.