Chip counting · mental arithmetic · worked examples
Roulette Dealer Payout Practice
This is a drill page, not a rules page. You get the number that landed, a few stacks on the layout and one job: work out what each winning stack is owed, what goes back to the player in total, and what the player actually made or lost on the spin.
A stack of 12 chips on 17 is one straight-up position. If 17 comes in, all twelve chips win together, but that is still one bet, not twelve. A spin produces exactly one winning pocket. What it can also produce is several overlapping positions that all happen to cover that pocket, and that is where the counting gets interesting.
Count positions first, then chips
Before touching a multiplier, sort out what is on the table. Three words need keeping straight. A position is a specific wager: straight 17, split 14–17, and so on. A stack is the pile of chips sitting on that position. The chip value is whatever that player’s colour was assigned at buy-in. Work with one player and one chip value at a time; mixing them is the quickest route to a wrong number.
- Note the winning pocket. On an American wheel, 0 and 00 are different pockets and settle separately.
- Find every position that includes that pocket. Look at where the chips physically sit on the layout, not at where the numbers sit on the wheel; the two have nothing to do with each other.
- Count the chips in each winning stack and multiply by that bet’s profit ratio.
- Add the winning stakes back in only when you want the total return.
- Subtract everything the player put down, losers included, when you want the overall result for the spin.
Everything here uses the standard ratios. How a dealer marks the winning number, sweeps the losing chips and pays in the right order is house procedure, and that isn’t something arithmetic can teach you.
Read “to one” and total return correctly
Payout ratios are quoted as profit. A straight bet paying 35:1 wins 35 units for every unit staked; the stake itself stays on the table (or goes back to the player), so what the player holds after the spin is 36. Count that stake once. Not twice, not zero times. Nearly every settlement error on this page comes down to that distinction, which is why three figures are kept apart throughout:
Each winning stack times its profit ratio, added up.
Profit on winners plus the winning stakes themselves.
Gross return minus every chip the player staked on the spin, winners and losers alike.
| Bet | Example position | Profit ratio | Total return |
|---|---|---|---|
| Straight | 17 | 35:1 | 36 units |
| Split | 14–17 | 17:1 | 18 units |
| Street | 16–17–18 | 11:1 | 12 units |
| Corner | 16–17–19–20 | 8:1 | 9 units |
| Six line | 13–14–15–16–17–18 | 5:1 | 6 units |
| Dozen / column | Second dozen: 13–24 | 2:1 | 3 units |
| Even money | Black | 1:1 | 2 units |
One bet is deliberately missing from that table. The American five-number bet (0, 00, 1, 2 and 3) pays 6:1 and loses when 17 lands, so it has no place in a list of winning positions for this example. A straight on 0 or 00 is nothing special either: it pays the ordinary 35:1 when that exact pocket comes in.
If you would rather take the ratios from a casino’s own rulebook, The Venetian’s roulette rules list them. For a fuller reference with a printable chart, use the payout calculator and chart. Games with special zero rules or random multipliers settle differently and need their own terms.
Break a multiplier into easier steps
Nobody multiplies by 35 in their head as a single operation. You take a route you trust, usually a round number plus or minus a correction, and then you check it a second way. For 35, 17 and 8, multiplying by a round number and subtracting the excess works well; for 11, adding one extra stack is cleaner. In the table, n is the number of winning chips on one position, all of the same value.
| Profit calculation | Equivalent method | Example: 7 winning chips |
|---|---|---|
| 35n | 40n − 5n, or 30n + 5n | 280 − 35 = 245 |
| 17n | 20n − 3n | 140 − 21 = 119 |
| 11n | 10n + n | 70 + 7 = 77 |
| 8n | 10n − 2n | 70 − 14 = 56 |
12 chips on straight 17
17 lands. There is one winning position: a stack of 12 chips at 1 unit each. Profit is 12 × 35 = 420 units; the player also gets the 12 chips back, so the total return is 432 units. With nothing else on the table, the net for the spin is +420.
9 chips on split 17–20
17 lands. The nine chips sitting on the line between 17 and 20 win. Profit is 9 × 17 = 153 units; total return is 162 units. Notice what this is: one winning split, paid on nine chips. It is not nine positions, and it is not two winning numbers. 20 didn’t land; the bet simply happened to cover it.
Three overlapping positions: work through the whole spin
Winning number: 17. Everything on the table belongs to one player, chips at 1 unit. The player has 2 chips on straight 17, 3 on split 14–17 and 4 on corner 16–17–19–20. Check the geometry before the arithmetic: 14 sits directly above 17 on the layout, and 16, 17, 19 and 20 form a square, so all three positions genuinely cover 17.
| Position | Chips | Profit on winner | Gross return |
|---|---|---|---|
| A · Straight 17 | 2 | 2 × 35 = 70 | 72 |
| B · Split 14–17 | 3 | 3 × 17 = 51 | 54 |
| C · Corner 16–17–19–20 | 4 | 4 × 8 = 32 | 36 |
| Total | 9 | 153 | 162 |
Now include a losing stack
Say the same player also dropped 5 chips on straight 2. When 17 lands, those five are swept. The total stake for the spin becomes 9 + 5 = 14 units, and the net is:
162 gross return − 14 total stake = +148 units net.
The 153 units of profit on the winning bets haven’t changed; that number is still right. It just isn’t the player’s result for the spin, because the losing stack has to come off. The short way gets you there too: 153 − 5 = 148. To check the settlement, enter the four positions in the multi-bet calculator and pick 17 as the result.
Use equal stacks as a counting shortcut
When two or more winning stacks are the same size, add the multipliers first and multiply once. It is quicker and, more to the point, easier to check. The catch is that the shortcut only holds if the stacks really are equal and the positions really are all winners. A pattern you recognise from training is no substitute for looking at what is actually on the cloth.
Example: 17 lands. There are 8 chips on straight 17 and 8 on corner 16–17–19–20, nothing else. Both positions win:
8 × (35 + 8) = 8 × 43 = 344 units of profit.
That is 16 winning chips, so gross return is 344 + 16 = 360. To check it from the other direction, use the return multipliers: 8 × (36 + 9) = 360, then take off the 16 staked units and you are back at 344.
Now put one more chip on that corner, making it a 9-chip stack. That single chip adds 8 units of profit and 9 units of return: profit becomes 352, gross 369, and the total stake is 17. The trap is finishing the sum with the old chip count still in your head after the stack has changed. Recount whenever a stack moves.
For the geometry of the larger overlapping packages, the called-bet breakdowns walk through each one. A word of caution: a tidy payout pattern is only a way of organising arithmetic. It doesn’t move the odds of the bet by a hair.
Convert chips to value without losing the remainder
Roulette table chips usually carry no printed value. A red chip is worth whatever the dealer marked it as for that player at buy-in, which is why you confirm the value before converting anything: the colour tells you whose chips they are, not what they are worth. The Venetian’s chip-value guidance covers why those chips stay tied to their table.
47 chips worth 5 units each, exchanged into 2-unit chips
Start with the value: 47 × 5 = 235 units. Divide by 2 and you get 117 whole chips with 1 unit left over:
117 × 2 + 1 = 235.
Round up to 118 chips and you have paid out 236 units; round down and forget the remainder and you have paid 234. Neither is right. The leftover unit has to be accounted for somewhere. Whether it goes back as a smaller chip or in some other permitted form is down to the table’s exchange procedure, but it doesn’t simply vanish.
Two players, two chip values
17 lands. Player A has a 3-chip stack on straight 17 at 2 units a chip: profit 3 × 35 × 2 = 210, gross 216. Player B has a 2-chip stack on split 17–20 at 5 units a chip: profit 2 × 17 × 5 = 170, gross 180. Neither has any other bets. Settle them one at a time. Pooling “five chips on 17” into a single calculation looks efficient and produces a number that belongs to nobody.
Eight payout practice questions
For each one, write down five things before opening the solution: how many winning positions, how many winning chips, profit on the winners, gross return, and overall net. Unless the question says otherwise, every chip is worth 1 unit and every bet belongs to the same player.
Exercise 1
17 lands. One stack of 7 chips is on straight 17. No other bets.
Show solution 1
One stack, one multiplier: 7 × 35 = 245. Add the 7 chips that come back.
1 winning position; 7 winning chips. Profit on winners: 245 units. Gross return: 252 units. Total stake: 7 units. Overall net: +245 units.
Exercise 2
20 lands. One stack of 13 chips is on split 17–20. No other bets.
Show solution 2
The split pays 17:1. Using 20n − 3n: 260 − 39 = 221, plus the 13 chips returned.
1 winning position; 13 winning chips. Profit on winners: 221 units. Gross return: 234 units. Total stake: 13 units. Overall net: +221 units.
Exercise 3
17 lands. One stack of 5 chips is on street 16–17–18. No other bets.
Show solution 3
A street pays 11:1: 5 × 11 = 55, with the 5 chips returned on top.
1 winning position; 5 winning chips. Profit on winners: 55 units. Gross return: 60 units. Total stake: 5 units. Overall net: +55 units.
Exercise 4
19 lands. One stack of 11 chips is on corner 16–17–19–20. No other bets.
Show solution 4
Corner, 8:1. Via 10n − 2n: 110 − 22 = 88, plus 11 returned.
1 winning position; 11 winning chips. Profit on winners: 88 units. Gross return: 99 units. Total stake: 11 units. Overall net: +88 units.
Exercise 5
15 lands. One stack of 6 chips is on six line 13–14–15–16–17–18. No other bets.
Show solution 5
Six line at 5:1: 6 × 5 = 30, and the 6 chips come back.
1 winning position; 6 winning chips. Profit on winners: 30 units. Gross return: 36 units. Total stake: 6 units. Overall net: +30 units.
Exercise 6
17 lands. A 2-chip stack is on straight 17, a 3-chip stack on split 14–17, and a 4-chip stack on corner 16–17–19–20. Another 5 chips are on straight 2.
Show solution 6
Same layout as the worked example above: 70 + 51 + 32 = 153 profit. Return is 153 + 9 = 162; then all 14 staked chips come off for the net.
3 winning positions; 9 winning chips. Profit on winners: 153 units. Gross return: 162 units. Total stake: 14 units. Overall net: +148 units.
Exercise 7
00 lands on an American wheel. A 2-chip stack is on straight 00. Each chip is worth 5 units. No other bets.
Show solution 7
Chip-equivalents first, then convert: 2 × 35 = 70, and 70 × 5 = 350 units of profit. Return is 72 chips × 5 = 360 units.
1 winning position; 2 winning chips. Profit on winners: 350 units. Gross return: 360 units. Total stake: 10 units. Overall net: +350 units.
Exercise 8
17 lands. An 8-chip stack is on straight 17 and an 8-chip stack on corner 16–17–19–20. No other bets.
Show solution 8
Equal stacks, so 8 × (35 + 8) = 344. Return 344 + 16 = 360.
2 winning positions; 16 winning chips. Profit on winners: 344 units. Gross return: 360 units. Total stake: 16 units. Overall net: +344 units.
Check the mistake, not just the final total
When a settlement comes out wrong, it is nearly always one of six things. Knowing which one saves you re-doing the whole spin.
- Right multiplier, wrong chip count: pay on the chips in the winning stack, not on the number of pockets the bet covers. A corner covers four numbers; that has nothing to do with how many chips are on it.
- Gross described as profit: 36 times a winning straight stake is what the player walks away with; 35 times is what they won.
- Winning stakes added twice: a return worked out with 36, 18 or 9 already includes the stake on that position. Don’t add it again.
- Losing bets left out: the player’s result for the spin subtracts everything they put down, not just the winning stakes.
- Wrong split or corner: positions have to share the right boundaries on the layout. Neighbours on the wheel are usually strangers on the cloth.
- Players or denominations mixed: finish one player’s value calculation before starting the next.
If the hard part is spotting which positions cover the number, spend time with the bet-placement guide; if it is the multiplier, keep the payout reference open. For a separate comparison of online table offerings and rules, see the casino comparison page.