Big or Small Bets: What a Two-Way Game Costs
A two-way bet looks like a coin flip. A small fee already makes it cost something, and one hidden rule can make it cost much more. Here is the arithmetic, with a table to check your own app against.
A coin flip with a fee
Big or small, odd or even, one colour or the other: these are two-way bets. Rounds of this kind are commonly described as paying 2× your stake when your side comes up and nothing when it does not. The calculator above starts from that picture as an illustration, not as any platform’s rules: a 50% chance of winning, a 2× payout and a 2% fee taken from each stake. The real chance, payout and fee are on your app’s rules screen, and those are the numbers to use.
With ₹100 a round for 60 rounds, the illustration stakes ₹6,000 and costs ₹120 on average. That is the house edge, 2.00%, applied to ₹6,000. A typical hour lands ± ₹759 from that average, and about 45 hours in 100 finish ahead.
Half is not quite enough to break even. With a 2× payout and a 2% fee you would need to win about 51.02% of rounds, where the calculator shows a house edge of 0.00%. Below that chance the game keeps something on average, and the next two sections show how fast the cost grows.
When one result makes both sides lose
Some two-way games are described with an exception: one kind of result that counts as a loss for both sides. In a three-dice game it could be a triple, with all three dice the same. In another game it could be a tie or a zero. We do not know whether this platform has any such rule. Its rules screen would say. What follows is an “if”.
Three dice give 216 possible throws. Say big means a total of 11 or more and small means 10 or less. Each side then gets 108 of the 216 throws, and three of each side’s 108 are triples (six triples in all, 2.78% of throws). If triples make both sides lose, each side keeps 105 throws of 216, a win chance of 48.61%.
In the calculator, that small drop moves the house edge from 2.00% to 4.72%. The expected loss for 60 rounds of ₹100 goes from ₹120 to ₹283. A rule with a bigger bite, one that left each side winning 45% of rounds, gives an edge of 11.80% and an expected loss of ₹708. That is the same edge as the violet and one-number illustrations on the Win Go cost page.
Win chance against house edge
Every row uses the same inputs: pays 2×, 2% fee, ₹100 a round, 60 rounds. Only the chance of winning changes.
| Your side wins | House edge | Expected loss, 60 rounds | Chance of finishing ahead |
|---|---|---|---|
| 51.02% (break-even) | 0.00% | ₹0 | 51% |
| 50% (the illustration) | 2.00% | ₹120 | 45% |
| 49% | 3.96% | ₹238 | 39% |
| 48.61% (if triples lose for both sides) | 4.72% | ₹283 | 36% |
| 48% | 5.92% | ₹355 | 33% |
| 47% | 7.88% | ₹473 | 28% |
| 45% | 11.80% | ₹708 | 18% |
| 40% | 21.60% | ₹1,296 | 4% |
Read the edge down the 50%, 49%, 48% and 47% rows: 2.00%, 3.96%, 5.92%, 7.88%. Each point of win chance lost adds about two points of house edge.
Now look at the swing. It reads ± ₹759 at a 50% chance and ± ₹755 at 45%, so it hardly moves. One hour cannot tell you which row your game belongs to. A game that wins 50% of rounds and one that wins 45% can both hand you a good hour. The cost shows only over many rounds.
How to check your own app
Open the game’s rules or “how to play” screen and look for answers to these:
- What happens on a tie, a zero, a triple, or any result that belongs to neither side? Does a bet on either side lose, get refunded, or pay less?
- Does “pays 2×” include your stake? In the calculator, Pays counts the stake, so even money is 2×.
- Is the fee taken from your stake or from your winnings, and how much is it?
- Does the screen give the chance of each result? If it lists every result and they are equally likely, count the ones where your side wins and divide by the total.
Then choose My own numbers and type your side’s chance of winning, its payout and the fee. If a result refunds your stake instead of losing it, add it as a second winning result that pays 1×. The tool takes the fee off every stake, refunds included, so if your app returns a stake in full, the real cost is a little lower than the tool shows. If the screens do not answer your questions, ask customer service from inside the platform’s own page and keep the reply.
What the table cannot tell you
We cannot see inside any platform, so we cannot say whether a given game has a tie, zero or triple rule, or what its true win chance is. The table shows what such a rule would cost if it exists, nothing more.
The expected-loss calculator page explains the other tiles. Cost per hour shows how round speed multiplies any of these edges, and the K3 dice guide lists every dice total for readers who want to count outcomes themselves.
Common questions
Is a big or small bet really a 50-50 chance?
In a plain two-way round, each side has an equal chance. The trouble starts when a rule lets one result beat both sides, such as a tie, a zero or a triple. Then each side wins less than half the time, and your app’s rules screen is where to check.
How much does one point of win chance cost?
In the illustration (2× payout, 2% fee), each point of win chance below 50% adds about two points of house edge: 2.00% at 50%, 3.96% at 49%, 5.92% at 48% and 7.88% at 47%.
What win chance breaks even at a 2× payout with a 2% fee?
About 51.02%. At that chance the calculator shows a house edge of 0.00%. Below it the game keeps something on average, and at 50% it keeps 2.00%.
Is odd or even different from big or small?
Not for the arithmetic. Any bet with two sides, the same payout and the same chance behaves the same way. What matters is the chance of winning after any special rule, the payout and the fee.
How do I enter a tie that refunds my stake?
Add it as a second winning result in the calculator, with its chance and a payout of 1×. The tool takes the fee off every stake, refunds included, so if your app returns the stake in full, your real cost is a little lower than shown.