Chip counting · mental arithmetic · worked examples
Roulette Dealer Payout Practice
Practise calculating winning stacks, mixed bets and chip values. Start with the number that landed, identify each winning position, then separate the profit paid on those bets from the stakes returned and the player’s overall result.
A stack of 12 chips on 17 is one straight-up position. If 17 lands, all 12 chips win. It is not 12 winning numbers. One spin produces one winning pocket, but several overlapping positions can win together.
Count positions first, then chips
Work with one player’s bets and one assigned chip value at a time. A position is a specific wager, such as straight 17 or split 14–17. A stack contains the chips placed on that position. The payout multiplier applies to every chip in the winning stack.
- Record the winning pocket, keeping 0 and 00 distinct.
- Identify each position that contains that pocket. Check the actual boundaries on the betting layout.
- Count the chips on each winning position and multiply by its profit ratio.
- Add the winning stakes back only when calculating the total return.
- Subtract every stake, including losing bets, when calculating the player’s overall net result.
These exercises use standard payouts. Table procedures determine how a dealer marks the result, clears losing bets and physically pays each player. Arithmetic practice alone does not establish those procedures.
Read “to one” and total return correctly
A straight bet paying 35:1 earns 35 units of profit for every winning unit staked. Its total return is 36 units because the winning stake is also retained or returned. Count that original stake once.
Add each winning stack multiplied by its profit ratio.
Profit on winners plus the value of the winning stakes.
Gross return minus the value of all bets placed on the spin.
| 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 |
The standard American five-number bet covers 0, 00, 1, 2 and 3 and pays 6:1. It loses when 17 lands, so it is not part of the winning-position table above. A straight on 0 or 00 pays the ordinary 35:1 when that exact pocket wins.
Standard ratios are listed in The Venetian’s roulette rules. For a broader reference and downloadable chart, use the payout calculator and chart. Special zero rules and multiplier games require their own settlement terms.
Break a multiplier into easier steps
Choose a decomposition you can check reliably. Multiplying by a round number and subtracting the excess is useful for 35, 17 and 8; adding one extra stack works neatly for 11. Here, n is the number of winning chips on a single 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. One position wins: a stack of 12 chips, each worth 1 unit. Profit is 12 × 35 = 420 units. The total return is 420 + 12 = 432 units. With no other bets, net is +420.
9 chips on split 17–20
17 lands. The stack of 9 chips on the shared boundary of 17 and 20 wins. Profit is 9 × 17 = 153 units; total return is 162 units. This is one winning split position, not nine positions or two winning numbers.
Three overlapping positions: work through the whole spin
Winning number: 17. All chips belong to one player and are worth 1 unit each. The player has 2 chips on straight 17, 3 on split 14–17 and 4 on corner 16–17–19–20. All three positions legally cover 17 on the standard layout.
| 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
Suppose the same player also placed 5 chips on straight 2. Those chips lose when 17 lands. The total stake was 9 + 5 = 14 units, so the overall net is:
162 gross return − 14 total stake = +148 units net.
The 153 units earned on the winning bets remain correct, but they are not the final net after the losing bet. Equivalently, 153 − 5 = 148. Enter the four positions in the multi-bet calculator and select result 17 to check the settlement.
Use equal stacks as a counting shortcut
When several winning positions have equal stacks, add their multipliers first. Keep the underlying positions explicit: a familiar pattern is useful only if it matches the bets actually on the table.
Example: 17 lands. There are 8 chips on straight 17 and 8 on corner 16–17–19–20, with no other bets. Both positions win:
8 × (35 + 8) = 8 × 43 = 344 units of profit.
There are 16 winning chips, so gross return is 344 + 16 = 360. A second check uses return multipliers: 8 × (36 + 9) = 360. Subtract the actual 16 staked units to recover 344.
Add one extra chip to the same corner, making that stack 9. It contributes another 8 units of profit and 9 units of return: the new profit is 352, gross is 369, and the total stake is 17. Do not subtract the old chip count after a stack changes.
For the geometry of larger overlapping packages, see the called-bet breakdowns. A payout pattern is a way to organise arithmetic; it does not make a bet more likely to win.
Convert chips to value without losing the remainder
Do not infer a universal denomination from a roulette chip’s colour. Confirm the value assigned to that player’s chips before converting a result. The Venetian’s chip-value guidance explains why those chips are tied to their table assignment.
47 chips worth 5 units each, exchanged into 2-unit chips
The original value is 47 × 5 = 235 units. Dividing by 2 gives 117 whole chips and a remainder of 1 unit:
117 × 2 + 1 = 235.
Rounding up to 118 chips would issue 236 units; rounding down and discarding the remainder would issue 234. Keep the remaining unit explicit. Whether it can be returned as a smaller chip or another permitted form depends on the table’s exchange procedure.
Two players, two chip values
17 lands. Player A has one 3-chip stack on straight 17, with each chip worth 2 units: profit 3 × 35 × 2 = 210, gross 216. Player B has one 2-chip stack on split 17–20, with each chip worth 5 units: profit 2 × 17 × 5 = 170, gross 180. Neither player has other bets. Keep their settlements separate rather than pooling five chips into one calculation.
Eight payout practice questions
Write down the winning-position count, winning chips, profit on winners, gross return and overall net before opening each solution. Unless a question gives another value, each chip is worth 1 unit and all bets belong to one player.
Exercise 1
17 lands. One stack of 7 chips is on straight 17. No other bets.
Show solution 1
7 × 35 = 245; add the 7 winning chips.
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
13 × (20 − 3) = 260 − 39 = 221; add 13.
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
5 × 11 = 55; add the 5 winning chips.
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
11 × (10 − 2) = 110 − 22 = 88; add 11.
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
6 × 5 = 30; add the 6 winning chips.
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
70 + 51 + 32 = 153. Return 153 + 9 = 162; subtract all 14 staked chips for 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
2 × 35 = 70 chip-equivalents of profit, worth 350 units. Return 72 × 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
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
- Right multiplier, wrong chip count: count the chips in the winning stack, not the number of covered pockets.
- Gross described as profit: 36 times a winning straight stake is the return; 35 times is the profit.
- Winning stakes added twice: a return calculated with 36, 18 or 9 already includes the stake on that position.
- Losing bets left out: subtract the player’s entire spin stake when reporting overall net.
- Wrong split or corner: positions must share the correct table boundaries. Numbers next to each other on the wheel are not necessarily adjacent on the betting layout.
- Players or denominations mixed: finish one player’s value calculation before starting the next.
Practise with the bet-placement guide when the difficulty is identifying positions, and use the payout reference when it is the multiplier. For a separate comparison of online table offerings and rules: https://roulettecalc.com/casinos/.