Kelly-based bankroll management
ZapankiSwap utilizes the Kelly Criterion for setting maximum bet sizes, employing 1x Kelly on the frontend and about 1.1x Kelly in the contracts to avoid transaction issues caused by fluctuations in bankroll size.
There is a minor departure from 1x/1.1x Kelly in two scenarios: (1) when individual users place maximum Kelly wager multibets, and (2) when maximum Kelly wagers from different wallets are placed simultaneously within a 30-second timeframe (subject to VRF). In such cases, if max wager multibets or simultaneous max wagers result in losses, Kelly decreases and the bankroll assumes slightly lower risk. Conversely, when users are winning, Kelly increases, and the bankroll assumes slightly higher risk.
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets.
Reaching the negative growth rate zone of 2x+ Kelly is highly unlikely, as it would require a long streak of consecutive wins with maximum wager bets, hitting the maximum multiplier, or an exorbitant amount of spending. The probabilities for such occurrences are extremely low and essentially considered impossible.
The likelihood of the bankroll reaching a negative growth rate of 2x+ Kelly is highly improbable. Even if it were to happen, it would only be temporary, occurring during instances when max Kelly wagers are placed in a single transaction or when other users' max Kelly wagers coincide within a ~30-second timeframe. Accepting bets at 2x+ Kelly in the short term is not necessarily detrimental, but it would lead to negative growth in the long run.
However, in the case of ZapankiSwap, the impact would be minimal, as the described probabilities are unlikely, and the bankroll should have already grown significantly by the time such events occur, keeping it above the initial value.
ZapankiSwap employs the Kelly criterion for bankroll management, using 1x Kelly on the frontend and 1.1x Kelly in the contracts to determine maximum wagers for single bets. However, there is a slight deviation in the max wager calculation for user multibets and simultaneous bets.
The strategy becomes less safe when the bankroll is losing and safer when winning. Due to the house edge, the strategy tends to be safer on average compared to the standard Kelly criterion. Reaching the negative growth region of 2x+ Kelly is highly unlikely and expensive, requiring significant losses or risking a large portion of the bankroll simultaneously.
Even if it were reached, it is not a long-term concern. In practice, the average bet size is expected to be lower than the max wager, further enhancing safety.