Bet-spread maths: what spreading your stake changes

The principle

A stake placed on a bet costs its expected loss, stake x house edge, whatever else you bet at the same time. When you spread 4 units over four spots, your expected loss is the sum of four small expected losses. The total stake is what drives the cost, not how it is split. What the split does change is the pattern of results: the hit rate, the size of a typical win and the width of the swings.

For the worked example we use the Crazy Time number bets with their base-wheel payouts: 1 pays 1 to 1, 2 pays 2 to 1, 5 pays 5 to 1 and 10 pays 10 to 1. The Top Slot multiplier and the bonus rounds are left out, so the figures show the shape of the outcomes, not the published RTP. Evolution's rules and wheel layout are on the Crazy Time odds page.

Reading plan B in detail

Plan B looks like insurance, but only one outcome in five finishes with a profit. Each segment of the wheel gives a different net result:

• 1 lands (21 of 54): you win 1 and lose 3, net -2.
• 2 lands (13 of 54): you win 2 and lose 3, net -1.
• 5 lands (7 of 54): you win 5 and lose 3, net +2.
• 10 lands (4 of 54): you win 10 and lose 3, net +7.
• A bonus segment (9 of 54): all four stakes lose, net -4.

So 34 of the 54 spins end in a loss even though you hold four bets, and the two most common results are the two that lose. Spreading raises the chance that one of your bets wins. It does not raise the chance that you come out ahead, because the smaller payouts cannot cover the other three stakes.

Plan A against plan C

Plan A wins often and wins small: 38.9% of spins end +4, the rest -4. Plan C is the opposite: it finishes ahead on 7.4% of spins and wins ten times as much when it does. Their swing sizes, 3.9 units against 11.5, show the difference. Over many spins plan C will spend its bankroll in a lumpier way. Neither is cheaper in the long run once the Top Slot and bonuses are included, because the long-run cost depends on the published RTP of each bet and on the total stake, not on how many spots you cover.

A practical consequence: if a session's purpose is to last longer, lower the stake. If its purpose is entertainment from large swings, concentrate and accept that most spins lose. Spreading across many spots rarely does either well.