For those who like calculating odds

Total value of all positions on the wheel divided by the number of positions on the wheel gives the average value of a win. Divide the average by the number of positions to give the chance of winning the average amount, convert to percent and then multiply by (average win divided by stake) to get your chance of winning something, subtract from 100 to give the House percentage.

I love how one video from @BigClive spun out this discussion. I'm going to include this exact example as an in class problem.

I get roughly the same as Glen from my own calculations for every £1 (50 x 2p) paid in: Blue: 50 * (9/25 * 4p) = £0.72 Red: 50 * (8/25 * 4p) = £0.64 Green: 50 * (4/25 * 8p) = £0.64 Yellow: 50 * (3/25 * 12p) = £0.72 White: 50 * (1/25 * 32p) = £0.64 Random: (72p+64p+64p+72p+64p)/5 = £0.672 For random selection, the house gets an average of 32.8p for every £1 paid in, i.e. 32.8%.

Seán Byrne

I agree. At first I had a silly number, but that was me being a betting virgin and not understanding the rules.

Mike Page

Random stays best if you increase to 10000 and 100000 spins. Of course, this does not simulate stopping if you have a big win at any point -- it forces you to play those 50 spins.

So I coded this in Python: https://replit.com/@GlenGilchrist/BigClive It simulates playing for 50 spins (2p per spin = £1 initial stake). It then simulates those 50 spins 1000 times. Using the numbers given, and starting with a £1 stake gives: Average after 1000 plays of 50 spins by betting on just b is... 71 Average after 1000 plays of 50 spins by betting on just r is... 64 Average after 1000 plays of 50 spins by betting on just g is... 63 Average after 1000 plays of 50 spins by betting on just y is... 72 Average after 1000 plays of 50 spins by betting on just w is... 62 Average after 1000 plays of 50 spins by betting randomly is... 62 So overall, the best strategy is to randomly pick a colour....

Of note: that's a vastly different table. Clive is only referring to the one he has.

Ryan Coleman

I think the house take is about 32%. Consider 25 punters each placing a bet and assume they distribute across colours proportionally to the number of slots of that colour. The total stake for one spin is 50p. The total payout varies between 32p and 36p. If blue: 9x4p, red: 8x4p, green: 4x8p, yellow: 3x12p, white: 1x32p. The weighted average payout is 33.92, so the house is taking 16.08p per spin. The assumption that punters distribute in the way I said could be wrong, but I think the rough order of magnitude is right for any reasonable assumption.

I used to work in an amusement arcade that had one of these machines. They have a row of 5 slots, one per colour, for each player. You can bet on 1-5 colours. These were the most reliable machines we had. They could also be converted to 10p per play by changing a plate per player.

Namirred

Ok so I am assuming all the positions (25) are potential winners? I.e there are no positions where only the house wins. So at 24 to 1 odds on each single position that gives you a 4% chance of winning on each position so that looks like this: 9 blue 16/9 36% 8 red 17/8 32% 4 green 21/4 16% 3 yellow 22/3 12% 1 white 24/1 4% On looking at payouts, clearly red is a bad deal as even though the odds are diminished you still only get the same payout as blue (if it was fair it would be 4.5p payout for red but since we don't have halfpennys thats impractical). Green as well is not good as it should be 9p rather than 8p but I suspect the machine only takes tuppences so doling out pennys as well would be impractical.

https://drive.google.com/file/d/13_VE-lw_uF5tJB4X-gEnT7DWRi7vstEh/view?usp=sharing I made a few calculations. For every 2 pence spent, the house keeps on average 1.6 pence

Loscha

“Just” 4%. Internet roulette if you’re gonna play, can get euro / “single 0”. In Vegas, unless you’re playing for large sums the roulette will have 0 and 00 greatly increasing the house advantage

Efault

Assuming players take the best bets the house expects to walk away with 28% of all money wagered .

I think the house take is more like 73%, unless I misunderstand the way it's played. The best bet is either blue (1.44p expected value) or yellow (same). Either way, you still expect to lose over a quarter of the money you put in! (Patreon makes it very hard to put the calculations in here, but it's about 2 minutes with a spreadsheet.)

if you pick blue - you have a 9/25 chance of getting 4p back. so it isn't a 100% win for the better.

Russell Peake

You choose a color before spinning the wheel, and you win only if the ball lands in that color.

Michael Dunn

I think I'm missing something. If it costs 2p to play and every position wins at least 4p, don't you always win? EDIT: wrong math was here

John Hiesey